CBSE Class 10 Mathematics Arithmetic Progression MCQs Set G

Question. Find t5 and t6 of the arithmetic progression 0, 1/4, 1/2, 3/4,……. respectively
(A) 1, 5/4 
(B) 5/4, 1
(C) 1, 7/4
(D) 7/4, 1

Answer: a

Question. If tn = 6n + 5, then tn + 1 =
(A) 6n –1
(B) 6n+11
(C) 6n + 6
(D) 6n – 5

Answer: b

Question. If n AMs are inserted between 2 & 38, the sum of the resulting series obtained is 200. The value of n (total number of terms) is
(A) 8
(B) 10
(C) 9
(D) 11

Answer: a

Question. The sum of first four terms of an A.P. is 56. The sum of last four terms is 112. If its first term is 11, find number of terms?
(A) 8
(B) 9
(C) 10
(D) 11

Answer: d

Question. If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
(A) ab/2(b-a)
(B) ab/(b-a)
(C) 3ab /2(b-a)
(D) none of these

Answer: c

Question. Find the 15 term of the arithmetic progression 10, 4, –2,……
(A) –72
(B) –74
(C) –76
(D) –78

Answer: b

Question. In a right triangle, the lengths of the sides are in arithmetic progression. If the lengths of the sides of the triangle are integers, which of the following could be the length of the shortest side?
(A) 1225
(B) 1700
(C) 1275
(D) 1150

Answer: c

Question. If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
(A) 1/n
(B) n-1/n
(C) n+1 /2n
(D) n+1 /n

Answer: d

Question. Which term of the arithmetic progression 21, 42, 63, 84, ……. is 420?
(B) 20
(C) 21
(D) 22

Answer: b

Question. The sum of the first 20 terms of an arithmetic progression whose first term is 5 and common difference is 4, is
(A) 820
(B) 830
(C) 850
(D) 860

Answer: d

Question. Find the smallest positive term of the series 25,22(3/4) ,20(1/2) ,18(1/4) ..............?
(A) 9th
(B) 10th
(C) 11th
(D) 12th

Answer: d

Question. Find the 15th term of the series 243, 81, 27,…….. 
(A) 1/314
(B) 1/38
(C) (1/3)9
(D) (1/3)10

Answer: c

Question. If the kth term of the arithmetic progression 25, 50, 75, 100,…….. is 1000, then k is ________.
(A) 20
(B) 30
(C) 40
(D) 50

Answer: c

Question. The sum of the first 51 terms of the arithmetic progression whose 2nd term is 2 and 4th tem is 8, is
(A) 3774
(B) 3477
(C) 7548
(D) 7458

Answer: a

Question. Three alternate terms of an arithmetic progression are x + y,x - y and 2x + 3y, then x =
(A) -y
(B) -2y
(C) -4y
(D) -6y

Answer: d

Question. Find the sum of all natural numbers and lying between 100 and 200 which leave a remainder of 2 when divided by 5 in each case.
(A) 2990
(B) 2847
(C) 2936
(D) none of these

Answer: a

Question. The sum of n terms of two A.P’s are in ratio 5n+ 4:9n+6 find ratio of their 18th terms?
(A) 179:321
(B) 180:322
(C) 170:320
(D) 171:329

Answer: a

Question. If S₁ is the sum of an arithmetic progression of ‘n’ odd number of terms and S₂ the sum of the terms of the series in odd places, then S₁ /S₂ =
(A) 2n/n+1
(B) n/n+1
(C) n+1/2n
(D) n+1/n

Answer: a

Question. If log2 (5X2^x+1) , log4 (2^1-x +1 ) and 1 are in A.P. find x?
(A) log₂⁵
(B) 1-log₂⁵
(C) log₅² 
(D) 1-log₅² 

Answer: b

Question. If S₁ = 3,7,11,15,........ upto 125 terms and S₂ 4,7,10,13,16........ upto 125 terms, then how many terms are there in S1 that are there in S2?
(A) 29
(B) 30
(C) 31
(D) 32

Answer: c

VERY SHORT ANSWER TYPE QUESTIONS

Question. Write the first three terms of an A.P. whose nth term is –3n + 5.
Answer: 2, –1, –4

Question. Find the number of terms of A.P. 7, 13, 19, ....., 301.
Answer: 50

Question. Which term of the A.P. 19, 18 , 1/5 , 17, 2/5 ,..... is the first negative term? 
Answer: 25th

Question. Given that the first term of an A.P. is 2 and its common difference is 4, find the sum of its first 40 terms.
Answer: 3200

Question. Write the missing terms of the A.P. –9, , –19, –24,
Answer: –14, –29

Question. The 17^th term of an A.P. exceeds its 10th term by 7. Find the common difference.
Answer: 1

Question. Which term of the A.P. 2, 6, 10, .... is 210?
Answer: 53rd

Question. How many 2-digit numbers are divisible by 3?
Answer: 30

Question. For what value of k, the numbers k + 2, 4k + 4 and 9k + 4 are three consecutive terms of an A.P.
Answer: k = 1

Question. Find a, such that –15, a, 35 are in A.P. 
Answer: a = 10

Question. If the sum of first n terms of an A.P. is 2n2 + 5n, write the sum of its first 5 terms.
Answer: 75

Question. Write the A.P. whose nth term is 4n – 7.
Answer:  –3, 1, 5, .....

Question. Is 67 a term of the A.P. 7, 10, 13, ......?
Answer: yes

Question. Write the 15^th term of an A.P. whose first term is 7 and the common difference is –3.
Answer:  –35

Question. Find the sum of first 50 natural numbers.
Answer: 1275

Question. Find the following sum : 1 + 3 + 5 + ..... 20 terms.
Answer: 400

Question. Find the sum to n terms of the A.P. whose rth term is 5r + 1.
Answer: n/2 (5n + 7)

Question. Find the sum of the odd numbers between 0 and 50.
Answer: 625

Question. Find the 10th term of an A.P. –3, -1/2 , 2,.... 
Answer: 39/2

Question. Find the sum of first 15 terms of an AP, whose nth term is 9–5n.
Answer: –465