Q 3) If an A.P. is 3, 5, 7, 9 ……. Find the 12th term of the A.P.
a) 12
b) 21
c) 22
d) 25
Ans: d
Q 4) If general term of an A.P. is 3n then find common difference.
a) 2
b) 3
c) 5
d) 6
Ans: b
Q 5) In A.P. 171, 162, 153, ………. Find first negative term.
a) 0
b) – 2
c) – 6
d) – 9
Ans: d
Q 6) Insert 4 numbers between 2 and 22 such that the resulting sequence is an A.P.
a) 4, 8, 12, 16
b) 5, 9, 13, 17
c) 4, 10, 15, 19
d) 6, 10, 14, 18
Ans: d
Q 7) If two numbers are 2 and 6 then find their arithmetic mean.
a) 3
b) 4
c) 5
d) 8
Ans: b
Q 8) The sum of n terms of two arithmetic progressions are in the ratio (2n – 7) : (7n + 5). Find the ratio of their 9th terms.
a) 4 : 5
b) 5 : 4
c) 9 : 31
d) 31 : 9
Ans: c
Q 9) If in an A.P., first term is 20, common difference is 2 and nth term is 42, then find n.
a) 10
b) 11
c) 12
d) 14
Ans: c
Q 10) If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
(a) a, b, c are in AP
(b) a², b², c² are in AP
(c) 1/1, 1/b, 1/c are in AP
(d) None of these
Ans: b
Solution
Given, 1/(b + c), 1/(c + a), 1/(a + b)
⇒ 2/(c + a) = 1/(b + c) + 1/(a + b)
⇒ 2b² = a² + c²
⇒ a², b², c² are in AP
Q 11) The sum of AP 2, 5, 8, ….. up to 50 terms is
(a) 3557
(b) 3775
(c) 3757
(d) 3575
Ans: b
Solution
Given, AP is 2, 5, 8, …..up to 50
Now, first term a = 2
common difference d = 5 – 2 = 3
Number of terms = 50
Now, Sum = (n/2) × {2a + (n – 1)d}
= (50/2) × {2 × 2 + (50 – 1)3}
= 25 × {4 + 49 × 3}
= 25×(4 + 147)
= 25 × 151 = 3775
Q 12) If 2/3, k, 5/8 are in AP then the value of k is
(a) 31/24
(b) 31/48
(c) 24/31
(d) 48/31
Ans: b
Solution
Given, 2/3, k, 5/8 are in AP
⇒ 2k = 2/3 + 5/8
⇒ 2k = 31/24
⇒ k = 31/48
So, the value of k is 31/48
Q 13) If the third term of an A.P. is 7 and its 7th term is 2 more than three times of its third term, then the sum of its first 20 terms is
(a) 228
(b) 74
(c) 740
(d) 1090
Ans: c
Solution
Let a is the first term and d is the common difference of AP
Given the third term of an A.P. is 7 and its 7th term is 2 more than three times of its third term
⇒ a + 2d = 7 ………….. (1)
and
3(a + 2d) + 2 = a + 6d
⇒ 3×7 + 2 = a + 6d
⇒ 21 + 2 = a + 6d
⇒ a + 6d = 23 ………….. (2)
From equation 1 – 2, we get
4d = 16 ⇒ d = 16/4 ⇒ d = 4
From equation 1, we get
a + 2×4 = 7 ⇒ a + 8 = 7 ⇒ a = -1
Now, the sum of its first 20 terms
= (20/2) × {2 × (- 1) + (20 – 1) × 4} = 10 × {- 2 + 19 × 4)}
= 10 × {- 2 + 76)} = 10 × 74 = 740
Q 14) If the sum of the first 2n terms of the A.P. 2, 5, 8, ….., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ….., then n equals
(a) 10
(b) 12
(c) 11
(d) 13
Ans: c
Explanation
Given, the sum of the first 2n terms of the A.P. 2, 5, 8, …..= the sum of the first n terms of the A.P. 57, 59, 61, ….
⇒ (2n/2) × {2 × 2 + (2n – 1) 3} = (n/2) × {2 × 57 + (n – 1)2}
⇒ n × {4 + 6n – 3} = (n/2) × {114 + 2n – 2}
⇒ 6n + 1 = {2n + 112}/2
⇒ 6n + 1 = n + 56
⇒ 6n – n = 56 – 1
⇒ 5n = 55
⇒ n = 55/5
⇒ n = 11
Q 15) If 7th and 13th
terms of an AP be 34 and 64
respectively, then its 18th term is
a) 87
b) 88
c) 89
d) 90
Ans: c
Q 16) If sum of p terms of an AP is q and sum of q terms is p then what is the sum of p + q terms
a) 0
b) p – q
c) p + q
d –(p + q)
Ans: d
Solution Hint: Find Sp = q and Sq = p and then
subtract these two
Q 17) If the sum of n terms of an AP be 3n2 – n and its common difference is 6, then its first term is
a) 2
b) 3
c) 1
d) 4
Ans: a
Q 18) The first and last term of an AP is 1 and 11. If the sum of its term is 36, then the number of terms will be
a) 5
b) 6
c) 7
d) 8
Ans: b
Q 19) If sum of its first n terms of an AP is 3n2
+ 5n then which of its term is 164 ?
a) 26th
b) 27th
c) 28th
d) None of these
Ans: b
