CBSE Class 11 Mathematics Sequences And Series Worksheet Set 01

Multiple Choice Questions

Question. The first five terms of the sequence, where a₁ = 3, a_n = 3a_n-1 + 2 for all n > 1 are
(a) 3, 15, 40, 110, 330
(b) 3, 11, 35, 107, 323
(c) 3, 20, 45, 110, 330
(d) 3, 11, 40, 107, 323
Answer : B

Question. In an AP, if K th term is 5K + 1. Then, the sum of first n terms is
(a) n/2(5n + 7)
(b) n/2(n + 7)
(c) n/2(n + 5)
(d) n/2(7n + 5)
Answer : A

Question. A person has 2 parents, 4 grandparents, 8 great grandparents and so on. Then, the number of ancestors during the ten generations preceding his own is
(a) 1084
(b) 2046
(c) 2250
(d) 1024
Answer : B

Question. The first five terms of the sequence a_n = (−1)^{n − 1}5^{n + 1} are
(a) 25, −125, 625, −3125, 15625
(b) 25, 125, 625, 3125, 15625
(c) 25, −125, 625, 3125, 15625
(d) 25, −125, 625, −3125, −15625
Answer : A

Question. Common ratio of four numbers of a GP in which the third term is greater than the first term by 9 and the second term is greater than 4th by 18 is
(a) 2
(b) −2
(c) 1
(d) −1
Answer : B

Question. The number of terms in the AP 7, 13, 19, …… 1205 are
(a) 30
(b) 34
(c) 31
(d) 10
Answer : B

Question. If the sum and product of three numbers of an AP is 24 and 440 respectively, then the common difference of the AP is
(a) ±1
(b) ±3
(c) ±2
(d) ±5
Answer : B

Question. A man starts repaying a loan as first instalment of ₹ 100. If he increases the instalment by ₹ 5 every month, then the amount he will pay in the 30th instalment is
(a) ₹ 241
(b) ₹250
(c) ₹245
(d) ₹265
Answer : C

Question. If the angles of any quadrilateral is in AP and their common difference is 10, then the angles are
(a) 75°, 85°, 95° and 105°
(b) 75°, 80°, 90° and 100°
(c) 75°, 85°, 90° and 105°
(d) 70°, 85°, 95° and 105°
Answer : A

Question. The sum of first three terms of a GP is 13/12 and their product is −1then the common ratio of the GP is
(a) −4/3 or −3/4
(b) 3/4 or 4/3
(c) 1/4 or −1/4
(d) 5/3 or −3/5
Answer : A

Question. 3^1/2 × 3^1/4 × 3^1/8 ×Kupto infinite,terms is equal to
(a) 3²
(b) 3
(c) 3³
(d) 3⁴
Answer : B

Asserion-Reasoning MCQs

Directions Each of these questions contains two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and
(d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false
(d) A is false; R is true.

Question. If nth term of a sequence is a_n = 2n² - n + 1
Assertion (A) First and second terms of same sequence are 2 and 7 respectively.
Reason (R) Third and fourth terms of same sequence are 16 and 29, respectively.
Answer : B

Question. Assertion (A) If the sequence of even natural number is 2, 4, 6, 8, …, then nth term of the sequence is an given by a_n = 2n , where n ∈ N.
Reason (R) If the sequence of odd natural numbers is 1, 3, 5, 7, …, then nth term of the sequence is given by a_n = 2n − 1, where n ∈ N.
Answer : B

Question. Assertion (A) The sum of first 6 terms of the GP 4, 16, 64, … is equal to 5460.
Reason (R) Sum of first n terms of the G. P is given by S_n = a(rⁿ - 1) / r - 1, where a = first termr = common ratio and |r| > 1.
Answer : A

Question. Assertion (A) The sum of first 23 terms of the AP 16, 11, 6, ...... is − 897.
Reason (R) The sum of first 22 terms of the AP x + y, x − y, x − 3y, ..... is 22 [x − 20y].
Answer : B

Question. Assertion (A) If the numbers -2/7, K, -7/2 are in GP, then k = ±1.
Reason (R) If a₁, a₂, a₃, are in GP, then a₂/a₁ = a₃/a₂
Answer : A

Question. Assertion (A) If the sum of first two terms of an infinite GP is 5 and each term is three times the sum of the succeeding terms, then the common ratio is 1/4.
Reason (R) In an AP 3, 6, 9, 12……… the 10th term is equal to 30.
Answer : B

Case Based MCQs

A company produces 500 computers in the third year and 600 computers in the seventh year. Assuming that the production increases uniformly by a constant number every year.

Based on the above information, answer the following questions.

(i) The value of the fixed number by which production is increasing every year is
(a) 25
(b) 20
(c) 10
(d) 30
Answer : A

(ii) The production in first year is
(a) 400
(b) 250
(c) 450
(d) 300
Answer : C

(iii) The total production in 10 years is
(a) 5625
(b) 5265
(c) 2655
(d) 6525
Answer : A

(iv) The number of computers produced in 21st year is
(a) 650
(b) 700
(c) 850
(d) 950
Answer : D

(v) The difference in number of computers produced in 10th year and 8th year is
(a) 25
(b) 50
(c) 100
(d) 75
Answer : B

Each side of an equilateral triangle is 24 cm. The mid-point of its sides are joined to form another triangle. This process is going continuously infinite.

Based on above information, answer the  following questions.

(i) The side of the 5th triangle is (in cm)
(a) 3
(b) 6
(c) 1.5
(d) 0.75
Answer : C

(ii) The sum of perimeter of first 6 triangle is (in cm)
(a) 569/4
(b) 567/4
(c) 120
(d) 144
Answer : B

(iii) The area of all the triangle is (in sq cm)
(a) 576
(b) 192√3
(c) 144√3
(d) 169√3
Answer : B

(iv) The sum of perimeter of all triangle is (in cm)
(a) 144
(b) 169
(c) 400
(d) 625
Answer : A

(v) The perimeter of 7th triangle is (in cm)
(a) 7/8
(b) 9/8
(c) 5/8
(d) 3/4
Answer : B

Q.1 Insert 6 numbers between – 6 and 29 such that the resulting sequence is an A.P.

Q.2 Find the sum of the series : 3 + 8 + 13 + ............... + 33

Q.3 Find the sum of odd integer from 1 to 21.

Q.4 Find the sum to n terms of the A.P., whose kth term is 5k + 1.

Q.5 If A1, A2, A3, …, An are n arithmetic means between a and b. Find the common difference between the terms.

Q.6 If the sum of n terms of an A.P. is 2mn + pn² , where m and p are constants, find the common difference.

Q.7 The ratio of the sums of m and n terms of an A.P. is m²: n². Show that the ratio of mth and nth term is (2m – 1): (2n – 1).

Q.8 Find the sum to n terms of the A.P., whose kth term is 5k + 1.

Q.9 Show that the sequence n2 - 3 is not an A.P.

Q.10 Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Q.11 What is the value of : 1²+2²+3²⁺ ..................+82?

Q.12 Find the sum of the series : 2 + 6 + 18 + .......... + 486

Q.13 Find the value of n so that may be the geometric mean between a and b.

Q.14 What is the 20th term of the sequence, defined by an = (n-1)(2-n)(3+n) ?

Q.15 Write the 16th term of the sequence defined by a_n = n² - n+1.

Q.16 Find the value of n so that aⁿ⁺¹ + ^bn+1 / aⁿ + bⁿ may be the geometric mean between a and b.

Q.17 The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour?

Q.18 If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq-r, br-p and cp-q = 1.

Q.19 If the fourth term of a G.P. is 3. Find the product of first 7 terms.

Q.20 Find the arithmetic mean of 6 and 12.

SECTION A:

1. Find the next two terms of the A.P given by: 2x – 3y, x – 4y , -5y, -x -6y, ……

2. How many terms are there in the sequence 4, 10, 16, 22, … 208?

3. Insert 4 arithmetic means between 4 and 29.

4. Solve for x : 2 + 5 + 8 + 11 + … + x = 345

5. If the sum of n terms of an A.P. is given by Sn = (3n2 + 4n) and its mth term is 49, then find m. 

6. Find the G.P. whose 4^th and 7^th terms are 1/18 and −1/486 respectively.

SECTION B:

7. Find the sum of first 24 terms of the A.P., if a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225

8. The ratio of the sums of n terms of two A.Ps is (7n +1) : (4n +27), find the ratio of their 11^th terms.

9. If a, b, c are in A.P, prove that (b+c)² – a² , (c+a)² – b² , (a+b)² – c² are also in A.P.

10. The product of 3 numbers in an A.P is 224 and the largest number is 7 times the smallest. Find the numbers.

11. If the roots of the equation (b-c) x² + (c-a) x + (a – b) = 0 are equal, then show that a, b, c are in A.P.

12. If the first term of an A.P is 2 and the sum of first 5 terms is equal to one-fourth of the sum of the next 5 terms, find the sum of first 30 terms.

13. The sum of first three terms of a G.P is 13/12 and their product is – 1 . Find the G.P.

14. The ratio of the sum of the first three terms is to that of first 6 terms of a G.P is 125 : 152. Find the common ratio.

15. If two geometric means g₁ and g₂ and one arithmetic mean A be inserted between two numbers, then show that 2A = 𝑔₁²/𝑔₂ + 𝑔²₂/𝑔₁

16. Find the sum to n terms of the series: 1/2×5 + 1/5×8 + 1/8×11+ ….

17. If 1/𝑥+𝑦 ,1/2𝑦, 1/𝑦+𝑧 are in A.P. Prove that x , y , z are in G.P.

18. If a, b, c are in A.P; b, c, d are in G.P and 1/𝑐, 1/𝑑, 1/𝑒 are in A.P. Prove that a, c, e are in G.P

19. Find the sum of all integers between 100 and 300 which are divisible by 2 or 5.

20. Find the sum to n terms of the series: 0.4 + 0.44 + 0.444 + …