CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set D

Question. The 19th term from the end of the series 2 + 6 + 10 + …. + 86 is:
a. 6
b. 18
c. 14
d. 10
Answer : C

Question. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th term, then its 13^th term is:
a. 0
b. – 1
c. – 12
d. – 13
Answer : A

Question. The n^th term of the series 3 + 10 + 17 + ….. and 63 + 65 + 67 + …… are equal, then the value of n is:
a. 11
b. 12
c. 13
d. 15
Answer : C

Question. The sum of the first and third term of an A.P. is 12 and the product of first and second term is 24, the first term is:
a. 1
b. 8
c. 4
d. 6
Answer : C

Question. If S_r denotes the sum of the first r terms of an A.P., then S_3r - S_r-1/S_2r - S_2r-1 is equal to:
a. 2r – 1
b. 2r + 1
c. 4r + 1
d. 2r + 3
Answer : B

Question. If the sum of the first 2n terms of 2, 5, 8…. is equal to the sum of the first n terms of 57, 59, 61…., then n is equal to:
a. 10
b. 12
c. 11
d. 13
Answer : C

Question. The sum of all odd numbers of two digits is:
a. 2475
b. 2530
c. 4905
d. 5049
Answer : A

Question. If sum of n terms of an A.P. is 3n² + 5n and 164 T_m = ,then m =?
a. 26
b. 27
c. 28
d. 29
Answer : B

Question. The sum of n terms of the series 1/1+√3 + 1/√3+v5

Answer : D

Question. If a₁, a₂ , ,.., a_n+1 + are in A.P., then 1a₁a₂ + 1/a₂a₃ + ..... + 1/a_na_n+1
a. n - 1 / a₁a_n+1
b. 1 / a₁a_n+1
c. n + 1 / a₁a_n+1
d. n / a₁a_n+1
Answer : D

Question. The number of terms in the series 101+ 99 + 97 +.....+ 47 is:
a. 25
b. 28
c. 30
d. 20
Answer : B

Question. The numbers (√2 +1),1, (√2 −1) will be in:
a. A.P.
b. G.P.
c. H.P.
d. None of these
Answer : B

Question. If x, 2x + 2,3x + 3 are in G.P., then the fourth term is:
a. 27
b. – 27
c. 13.5
d. – 13.5
Answer : D

Question. The first term of an infinite geometric progression is x and its sum is 5. Then:
a. 0 ≤ x ≤ 10
b. 0 < x < 10
c. −10 < x < 0
d. x > 10
Answer : B

Question.

a. e + 1
b. e – 1
c. 1 – e
d. e
Answer : B

Question. The G.M. of the numbers 2 3 3,3 , 3 ......3n is:
a. 3^2/n
b. 3^n+1/2
c. 3^n/2
d. 3^n−1/2
Answer : B

Question. The two geometric mean between the number 1 and 64 are:
a. 1 and 64
b. 4 and 16
c. 2 and 16
d. 8 and 16
Answer : B

Question. The 4th term of a H.P. is 3/5 and 8th term is 1/3 then its 6th term is:
a. 1/6
b. 3/7
c. 1/7
d. 3/5
Answer : B

Question. The harmonic mean of the roots of the equation 2 (5 + √2)x − (4 +√3) x +8 + 2 √3 = 0 is:
a. 2
b. 4
c. 6
d. 8
Answer : B

Question. If a,b,c are in H.P., then the value of (1/b + 1/c - 1/a) (1/c + 1/a - 1/b)
a. 2/bc + 1b²
b. 3/c² + 2/ca
c. 3/b² - 2b ab
d. None o]f these
Answer : C

Question. 1 + 3 /22  5/22  ∞ is equal to:
a. 3
b. 6
c. 9
d. 12
Answer : B

Question. Sum of the series 2 3 99 1+ 2.2 + 3.2 + 4.2 +....+100.2 is:
a. 100.2¹⁰⁰+1
b. 100 99.¹⁰⁰ +1
c. 100 99.¹⁰⁰ −1
d. 100 100.¹⁰⁰ −1
Answer : B

Question. The sum to n terms of the series 1 + 3 + 7 + 15 + 31 +...is:
a. 2_n+1 − n
b. n n + − −
c. 2_n - n − 2
d. None of theseSummation of Series
Answer : B

Question. If the A.M., G.M. and H.M. between two positive numbers a and b are equal, then:
a. a = b
b. ab = 1
c. a > b
d. a < b
Answer : A

Question. If 5 7 9 x = log 3+ log 5 + log 7 then:
a.x > 3/2
b .x > 3/2
c. > 1/13 
d.1/√3
Answer : C

Question. If the A.M. of two numbers is greater than G.M. of the numbers by 2 and the ratio of the numbers is 4 : 1, then the numbers are:
a. 4, 1
b. 12, 3
c. 16, 4
d. None of these
Answer : C

Question. If the ratio of H.M. and G.M. of two quantities is 12 : 13, then the ratio of the numbers is:
a. 1: 2
b. 2: 3
c. 3: 4
d. None of these
Answer : D

Question. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation:
a. 2 x −18x −16 = 0
b. 2 x −18x +16 = 0
c. 2 x +18x −16 = 0
d. 2 x +18x +16 = 0
Answer : B

Question. If the arithmetic, geometric and harmonic means between two positive real numbers be A, G and H , then:
a. A² = GH
b. H² = AG
c. G = AH
d. G² = AH
Answer : D

Question. If log , log , log a b c x x x be in H.P., then a, b, c are in:
a. A.P.
b. H.P.
c. G.P.
d. None of these
Answer : C

Question. If a, b, c are in A.P. as well as in G.P., then:
a. a = b ≠ c
b. a ≠ b = c
c. a ≠ b ≠ c
d. a = b = c
Answer : D

Question. If a, b, c are in G.P., a − b, c − a, b − c are in H.P., then a + 4b + c is equal to:
a. 0
b. 1
c. −1
d. None of these
Answer : A

Question. If A₁, A₂ are the two A.M.'s between two numbers a and b and  G₁ ,G₂ be two G.M.'s between same two numbers, then A₁ + A₂ / G₁,G₂ = ?
a. a+b/ab
b. 2+b/2ab
c. 2ab/a+b
d. ab/a+b
Answer : A

Question. If G.M. = 18 and A.M. = 27, then H.M. is:
a. 1/18
b. 1/12
c. 12
d. 9√6
Answer : C

Question. If 9 A.M.'s and H.M.'s are inserted between the 2 and 3 and if the harmonic mean H is corresponding to arithmetic mean A , then A + 6/H = ?
a.1
b.3
c.5
d.6
Answer : C

Question. If | x |<1, then the sum of the series 1+ 2x + 3x³ + 4x³ + ...∞ will be:
a. 1/1 − x
b. 1/1 + x
c. 1/(1 + x)²
d. 1/(1- x)²
Answer : D

Question. The sum of infinite terms of the following series 1 + 4 / 5 + 7 / 5² + 10 / 5³
a. 3/16
b. 35/8
c. 35/4
d. 35/16
Answer : 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. Sum of n terms of series 12 + 16 + 24 + 40 + ..... will be:
a. 2(2ⁿ − 1) + 8n
b. 2(2ⁿ − 1) + 6n
c. 3(2ⁿ − 1) + 8n
d. 4(2ⁿ − 1) + 8n
Answer : D

Question. The sum of the series 1 + 1.3 / 6 + 1.3.5 / 6.8 + ∞ is:
a. 1
b. 0
c. ∞
d. 4
Answer : D

Question. The sum of the series 1 + 2x + 3x² + 4x³ +......... upto n terms is:

Answer : A

Question. If the set of natural numbers is partitioned into subsets S₁ = {1}, S₂ = {2, 3}, S₃ = {4, 5, 6} and so on. Then the sum of the terms in S₅₀ is:
a. 62525
b. 25625
c. 62500
d. None of these
Answer : A

Question. The sum first n odd natural number is
(a) 2n-1
(b) n²
(c) 2n+1
(d) n²-1
Answer : B

Question. The next term of an AP √7 , √28 , √63 , ………..
(a) √84
(b) √70
(c) √97
(d) √112
Answer : A

Question. For the A.P. 3/2 , 1/2 , -1/2 , -3/2 write common difference
(a) 1
(b) 14
(c) -1
(d) 3/2
Answer : C

Question. What is common difference of an AP . in which a₁₈ – a₁₄ = 32
(a) 8
(b) -8
(c) -4
(d) 4
Answer : A

Question. If 6/5, a , 4 are in AP then value of a is
(a) 13/3
(b) 13/6
(c) 13/5
(d) 13/7
Answer : C

Please click on below link to download CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set D