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Students can refer to the following Sequences and Series Class 11 MCQ Question with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Sequences and Series Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Sequence and Series Class 11 MCQ Question with Answers

We have provided below Sequences and Series Class 11 MCQ Question with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Class 11 Sequence and Series MCQ pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**Question. The product of first nine terms of a GP is, in general, equal to which one of the following? **

(a) The 9th power of the 4th term

(b) The 4th power of the 9th term

(c) The 5th power of the 9th term

(d) The 9th power of the 5th term

**Answer**

D

**Question. In a G.P. if (m + n)th terms is p and (m – n)th term is q, then mth term is: **

(a) p/q

(b) q/p

(c) pq

(d) √pq

**Answer**

D

**Question. A sequence containing a finite number of terms is called a………………. **

(a) Finite sequence

(b) A.P. sequence

(c) G.P. sequence

(d) General sequence

**Answer**

A

**Question. The third term of a geometric progression is 4. **

The product of the first five terms is :

(a) 43

(b) 45

(c) 44

(d) 47

**Answer**

B

**Question. In an AP. the pth term is q and the (p + q)th term is 0. Then the qth term is **

(a) – p

(b) p

(c) p + q

(d) p – q

**Answer**

B

**Question. If roots of the equation x3 – 12x ^{2} + 39 x – 28 = 0 are in AP, then its common difference is **

(a) ± 1

(b) ± 2

(c) ± 3

(d) ± 4

**Answer**

C

**Question. If a, b, c, d, e, f are in A.P., then e – c is equal to: **

(a) 2(c – a)

(b) 2(d – c)

(c) 2(f – d)

(d) (d – c)

**Answer**

B

**Question. The fourth, seventh and tenth terms of a G.P. are p, q, r respectively, then : **

(a) p^{2} = q^{2} + r^{2}

(b) q^{2} = pr

(c) p^{2} = qr

(d) pqr + pq + 1 = 0

**Answer**

B

**Question. A man saves ₹135/- in the first year, ₹150/- in the second year and in this way he increases his savings by ₹15/- every year. In what time will his total savings be ₹5550/-? **

(a) 20 years

(b) 25 years

(c) 30 years

(d) 35 years

**Answer**

A

**Question. The A. M. between two positive numbers a and b is twice the G. M. between them. The ratio of the numbers is **

(a) (√2 + 3) : (√2 – 3)

(b) (2 + √3 ) : (2 – √3 )

(c) ( √3 + 1) : ( √3 – 1)

(d) None of these

**Answer**

B

**Question. If 1, a and P are in A. P. and 1, g and P are in G. P., then **

(a) 1 + 2a + g^{2} = 0

(b) 1 + 2a – g^{2} = 0

(c) 1 – 2a – g^{2} = 0

(d) 1 – 2a + g^{2} = 0

**Answer**

D

**Question. For a, b, c to be in G.P. What should be the value of a-b /b-c ? **

(a) ab

(b) bc

(c) a/b or b/c

(d) None of these

**Answer**

C

**Question. What is the sum of terms equidistant from the beginning and end in an A.P. ? **

(a) First term – Last term

(b) First term × Last term

(c) First term + Last term

(d) First term ¸ Last term

**Answer**

C

**Question. Find 4th term from the end of the G.P. 3, 6, 12, 24., ………., 3072. **

(a) 348

(b) 843

(c) 438

(d) 384

**Answer**

D

**Question. If ax = by = cz, where a, b, c are in G.P. and a,b, c, x, y, z ¹ 0; then x, y, z are in: **

(a) A.P.

(b) G..P.

(c) H.P

(d) none of these

**Answer**

C

**Question. If a, b, c are in G.P. then 1/a ^{2}-b^{2} + 1/b^{2} is **

(a) 1/c

^{2}– b

^{2}

(b) 1/b

^{2}-c

^{2}

(c) 1/c

^{2}– a

^{2}(d) 1/b

^{2}-a

^{2}

**Answer**

B

**Question. The value of 3 –1 + 1/3 – 1/9 +……….is equal to: **

(a) 20/9

(b) 9/20

(c) 9/4

(d) 4/9

**Answer**

C

**Question. If the pth, qth and rth terms of a G.P. are again in G.P., then which one of the following is correct? **

(a) p, q, r are in A.P.

(b) p, q, r are in G.P.

(c) p, q, r are in H.P.

(d) p, q, r are neither in A.P. nor in G.P. nor in H.P.

**Answer**

A

**Question. Let a _{1}, a_{2}, a_{3}, ………..be the sequence, then the sum expressed as a_{1} + a_{2 }+ a_{3} + …… + an is called …….. **

(a) Sequence

(b) Series

(c) Finite

(d) Infinite

**Answer**

B

**Question. A sequence may be defined as a **

(a) relation, whose range Í N (natural numbers)

(b) function whose range Í N

(c) function whose domain Í N

(d) progression having real values

**Answer**

C

**Question. If 5 (3 ^{a – 1} + 1), (6^{2a – 3} +2) and 7(5^{a – 2} + 5) are in AP, then what is the value of a? **

(a) 7

(b) 6

(c) 5

(d) none

**Answer**

D

**Question. If x + 1, 4x + 1, and 8x + 1 are in geometric progression, then what is the non-trivial value of x ? **

(a) – 1

(b) 1

(c) 1/8

(d) 1/4

**Answer**

C

**Question. The 10 th common term between the series 3 + 7 + 11 + …. and 1 + 6 + 11 + …. is **

(a) 191

(b) 193

(c) 211

(d) None of these

**Answer**

A

**Question. If p, q, r are in A.P., a is G.M. between p and q and b is G.M. between q and r, then a ^{2}, q^{2}, b^{2} are in **

(a) G.P.

(b) A.P.

(c) H.P

(d) None

**Answer**

B

**Question. If p ^{th} term of an AP is q, and its q^{th} term is p, then what is the common difference ? **

(a) – 1

(b) 0

(c) 2

(d) 1

**Answer**

A

**Question. Let x be one AM and g _{1} and g_{2} be two G.Ms between y and z. What is g_{1}^{3} + g_{2}^{3} equal to ? **

(a) xyz

(b) xy

^{2}z

(c) xyz

^{2}

(d) 2xyz

**Answer**

D

**Question. If 1, x, y, z, 16 are in geometric progression, then what is the value of x + y + z ? **

(a) 8

(b) 12

(c) 14

(d) 16

**Answer**

C

**Question. In a Geometric Progression with first term a and common ratio r, what is the Arithmetic Mean of the first five terms? **

(a) a + 2r

(b) a r2

(c) a (r5 – 1)/[5(r – 1)]

(d) a (r4 – 1)/[5(r – 1)]

**Answer**

C

**Question. What is the sum of the first 50 terms of the series (1 × 3) + (3 × 5) + (5 × 7) + …. ? **

(a) 1,71,650

(b) 26,600

(c) 26,650

(d) 26,900

**Answer**

A

**Question. If a, b, c are in geometric progression and a, 2b,3c are in arithmetic progression, then what is the common ratio r such that 0 < r < 1 ? **

(a) 1/3

(b) 1/2

(c) 1/4

(d) 1/8

**Answer**

A

**Question. Let bi > 1 for i = 1, 2,…,101. Suppos logeb _{1},logeb_{2},…logeb_{101} are in Arithmetic Progression (A.P.) with the common difference loge 2. Suppose a_{1},a_{2}….a_{101} are in**

**A.P. such that a1=b1 and a51=b51**

.If t = b1 + b2 +…+ b51 and

1 2 51 s = a + a +….+ a , then :

a. s > t anda101 > b101

b. s > t and a101 < b101

c. s < t and a101 > b101

d. s < t and a101 <b101

**Answer**

B

**Question. Let **

a. 1056

b. 1088

c. 1120

d. 1332

**Answer**

A,D

**Question. 1+ 3+ 7 +15 + 31+………. to n terms = ? **

a. 2n+1 − n

b. 2n+1 − n−2

c. 2n − n−2

d. None of these

**Answer**

B

**Question. Let a =1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5. Then:**

a. 55 ≥ a

b. 3 3 ≥ 5!

c. 55 ≥ 6a

d. none of these

**Answer**

A,B

**Question. Let S1,S2…be squares such that for each n ≥1, the length of a side of S _{n} B,C,**

**equals the length of a diagonal of Sn+1. If the length of a side of S1is 10cm, then for which of the following values of n is the area of Sn less 1sq cm2 than:**

a. 7

b. 8

c. 9

d. 10

**Answer**

D

**Question. The sum of n terms of the series **

**Answer**

A,C

**Assertion and Reason**

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:

a. If both assertion and reason are true and the reason is the correct explanation of the assertion.

b. If both assertion and reason are true but reason is not the correct explanation of the assertion.

c. If assertion is true but reason is false.

d. If the assertion and reason both are false.

e. If assertion is false but reason is true.

**Question. The natural numbers are divided into rows as follows: **

Assertion: Sum of the numbers in the 10th row is a number which can be written as sum of two cubes in two different ways.

Reason: Sum of the numbers in the rth row is

**Answer**

C

**Question. Suppose a2,b2,c2 are in A.P. **

**Answer**

D

**Question.** **Assertion: **

for each n, then, a1 ,a2 ,a3 … are in A.P D

Reason: Sum to n terms of an A.P. is always of the form an2 + bn.

**Answer**

D

**Question.** Assertion: The largest interval for which we can find the sum of the series +(2x−1) +(2x−1)2 +(2x−1)3 +… is (0, 1)

Reason: An infinite geometric series 2 a + ar + ar +… can be summed up if | r | <1.

**Question.** Assertion: If a, b, c > 0 and the expression (a + c)x2

√(a + c)2 + 4b2 )x + b > 0 ∀ x∈R, then a,b,c are in G.P.

Reason: 2 ax + bx + c > 0 ∀ x∈R if and only if a > 0 and b2 − 4ac < 0.

**Answer**

D

**Question. Let α ,β be roots of 2 ax + 2bx + c = 0 and 2 ) = b − ac. **

Assertion: If α +β ,α2 + β2 ,α3 +β3 are in G.P. then c) = 0

Reason: If α ,αβ ,β are in A.P. then b + c = 0.

**Answer**

B

**Question. Suppose four distinct positive numbers a1 ,a2 ,a3 ,a4 are in G.P. ****Let b1 = a1 ,b2 = b1 + a2 ,b3 = b2 + a3 and b4 = b3 + a4 .**

Assertion: The numbers b1 ,b2 ,b3 ,b4 are neither in A.P. nor in G.P.

Reason: The numbers b1 ,b2 ,b3 ,b4 are in H.P.

**Answer**

C

**Question. Let a, b, c, d, e be five non-zero numbers such that a, b, c are in A.P., b, c, d are in G.P., and c, d, e are in H.P.? **

Assertion: If a = 2,e =18,b > 0, then b = 4 and c = 6.

Reason: If a = 2,e =18,c = −6, then b < 0.

**Answer**

B

**Question. Suppose a, b, c, d are four real number and**

**Assertion: **If a, b, c, d are in A.P. and ∫02)△(x)dx = −4, then common difference of the A.P. is ± 1.**Reason:** If a,b,c,d are in A.P., then △(x) is independent of x.

**Answer**

B

**Question. Suppose four distinct positive numbers a1 , a2 ,a3 ,a4 are in **

GP. Let b1 = a1 ,b2 = b1 + a2 ,b3 = b2 + a3 and b4 = b3 + a4

Assertion: The numbers b1 ,b2 ,b3 ,b4 are neither in AP nor in GP.

Reason: The numbers b1 ,b2 ,b3 ,b4 are in HP

**Answer**

C

**Question.** **Assertion: **The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) is 800.

**Answer**

A

**Paragraph –I**

Let r V denotes the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common

difference is (2r – 1). Let Tr = Vr+1 − Vr − 2 = and Qr = Tr+1 − Tr = for r = 1, 2, …

**Question. Tr is always: **

a. an odd number

b. an even number

c. a prime number

d. a composite number

**Answer**

D

**Question. Which one of the following is a correct statement? **

a. Q1 , Q2, Q3,…are in AP with common difference 5

b. Q1 , Q2, Q3,…are in AP with common difference 6

c. Q1 , Q2, Q3,…are in AP with common difference 11

d. Q1 = Q2= Q3= …

**Answer**

B

**Paragraph –II**

Let A1, G1, H1 denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n ≥ 2,

let An – 1 and Hn – 1 has arithmetic, geometric and harmonic means as An, Gn, Hn respectively.

**Question. Which one of the following statements is correct ? **

a. G1 > G2 > G3 > …

b. G1 < G2 , < G3 > …

c. G1 = G2 = G3 = …

d. G1 < G3 < G3 < … and G2 > G4 > G6 > …

**Answer**

A

**Question. Which of the following statements is correct ? **

a. A1 > A2 >…

b. A1 < A2 < A3 < ….

c. A1 > A3 > A5 > …. and A2 < A4 < A6 < ….

d. A1 < A3 < A5 < ….and A2 > A4 > A6 > ….

**Answer**

A

**Question. Which of the following statements is correct ? **

a. H1 > H2 > H3 > ….

b. H1 < H2 < H3 < ….

c. H1 > H3 > H5 > ….and H2 < H4 < H6 < ….

d. H1 < H3 < H5 < ….and H2 > H4 > H6 > ….

**Answer**

B

**Paragraph –III**

Let an denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = The number of such n-digit integers ending with digit 1 and cn =

The number of such n-digit integers ending with digit 0.**Match the Column Answer: If a^{n+1} + b^{n+1}/a^{n} + b^{n} then: **

a. A→2, B→3, C→1

b. A→1, B→2, C→3

c. A→3, B→2, C→1

d. A→3, B→1, C→2

**Answer**

A

**Question. Match the statement of Column I with those in Column II: **

a. A→4, B→1, C→5, D→3, E→2

b. A→4, B→2, C→3, D→5, E→1

c. A→2, B→3, C→5, D→1, E→4

d. A→ 5, B→ 1, C→4, D→3, E→2

**Answer**

B

**Question. Which of the following is correct ? **

a. a17 = a16 + a15

b. a17 ≠ a16 + a15

c. b17 ≠ b16 + c16

d. a17 = c16 + b16

**Answer**

A

**Question. The value of b6 is: **

a. 7

b. 8

c. 9

d. 11

**Answer**

B

**Question. a, b, c∈R and a, b, c are in A.P. math the entries of column I with those of column II:**

a. A→1, B→1, C→1.2.3, D→4

b. A→1, B→2, C→1.4.3, D→3

c. A→2, B→3, C→1.2.3, D→4

d. A→1, B→3, C→1.2.3, D→2

**Answer**

A

**Question. If **

** then the least value of n must be: **

## Answer

8

**Question. If (1) (2010) + (2) (2009) + (3) (2008) + . . .+ (2010) (1) = (335) (2011) (λ), then the value of λ must be: **

## Answer

2021

**Question. If **

## Answer

2008

**Question. If a, b, c are in HP and if (a+2b/2a−b) + (C+b/2c−b) > √λ√λ√λ…..∞ then the value of λ must be : **

## Answer

4

**Question. Let Sk, k = 1,2…100 denote the sum of the infinite geometric series whose first term is k–1/k! nd the common ratio is 1/k. Then the value of 100 ^{2}/100!**

## Answer

4

**Question. The minimum value of the sum of real numbers a−5 , a−4 , 3a−3 ,1, a8 and a10 a with a > 0 is: **

## Answer

8

**Question. A pack contains n card numbered from 1 to n. Two consecutive numbered card are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k – 20 is equal to: **

## Answer

5

**Question. Let a, b, c be positive integers such that b/a is an integer. If a,b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of a2 + a−14/a+1 is: **

## Answer

4

**Question. Let a1,a2,a3,…a11 be real numbers satisfying a1=15,27–2a2 > 0 and ak = 2ak−1−ak−2 for k = 3,4……11 IF a12 + a22 +…..a112 /11 = 90, then the value of a1+ a2+…..a11 / 11 is equal to: **

## Answer

0

**Question. Let a1 , a2 , a3 , …, a100 be an arithmetic progression with a1 = 3 and**

** For any integer n with 1≤ n ≤ 20, let m = 5n. If Sm/Sn does not depend on n, then an is: **

## Answer

3,9

**Question.**

**then the value of (logy x)5 must be : **

## Answer

3125

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