Arithmetic Progression (A.P.) Questions and Answers

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Arithmetic Progression(A.P.) – 1”.

1. A sequence is called ___________________ if a_n+1 = a_n + d.
a) arithmetic progression
b) geometric Progression
c) harmonic Progression
d) special Progression
View Answer

Answer: a
Explanation: A sequence is called arithmetic progression if a_n+1 = a_n + d where a₁ is the first term and d is common difference.

2. What is n^th term of an A.P.?
a) a_n = a + (n-1) d
b) a_n = a + (n) d
c) a_n = a*r^n-1
d) a_n = a*rⁿ
View Answer

Answer: a
Explanation: Since every term of an A.P. is incremented by common difference d.
i.e. a_n+1 = a_n + d = a_n-1 + 2d = ……. = a₁ + n*d
or a_n = a + (n-1) d

3. If an A.P. is 3,5,7,9……. Find the 12^th term of the A.P.
a) 12
b) 21
c) 22
d) 25
View Answer

Answer: d
Explanation: From the given A.P., a=3 and d=5-3 =2.
We know, a_n= a + (n-1) d => a₁₂ = a+11d = 3+11*2 = 3+22 = 25.

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4. If a constant is added or subtracted from each term of an A.P. then resulting sequence is also an A.P.
a) True
b) False
View Answer

Answer: a
Explanation: Let x be the constant which is added to each term of an A.P., then a_n’ = a_n + x and a’ = a + x. So n^th term will be a_n’ = a_n + x = a+(n-1) d + x = (a + x) + (n-1) d = a’ + (n-1) d which is n^th term of an A.P. If x is negative it is case of subtraction.

5. If a constant is multiplied to A.P. then resulting sequence is also an A.P.
a) True
b) False
View Answer

Answer: a
Explanation: Let x be the constant which is multiplied to each term of an A.P., then a_n’ = a_n * x and a’ = a * x. So n^th term will be a_n’ = a_n * x = (a+(n-1) d) * x = (a * x) + (n-1) d x = a’ + (n-1) x d which is n^th term of an A.P.

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6. If 3^rd term of an A.P. is 6 and 5^th term of that A.P. is 12. Then find the 21^st term of that A.P.
a) 40
b) 42
c) 60
d) 63
View Answer

Answer: c
Explanation: Given, a₃ = 6 and a₅ = 12.
=> a + 2d = 6 and a + 4d = 12
=> 2d = 6 => d=3.
=> a + 2*3 = 6 => a=0
So, a₂₁ = a + 20 d = 0 + 20*3 = 60.

7. If sum of n terms of an A.P. is n²+5n then find general term.
a) n+1
b) 2n
c) 3n
d) n²+3n
View Answer

Answer: b
Explanation: Given, S_n = n²+5n
We know, a_n = S_n– S_n-1 = (n²+5n) – ((n-1)²+5(n-1)) = (n²+5n) – (n²+1-2n+5n-1) = 2n.

8. If an A.P. is 1,7,13, 19, ……… Find the sum of 22 terms.
a) 127
b) 1204
c) 1408
d) 1604
View Answer

Answer: c
Explanation: From the given A.P., a=1 and d=7-1 = 6.
We know, S_n = \(\frac{n}{2} (2a+(n-1)d)\)
S₂₂ = \(\frac{22}{2} (2*1+(22-1)6)\) = 11(2+21*6) = 11(2+126) = 11*128 = 1408.

9. If in an A.P., first term is 20 and 12^th term is 120. Find the sum up to 12^th term.
a) 420
b) 840
c) 140
d) 1680
View Answer

Answer: b
Explanation: Given, a=20, a₁₂= 120, n=12.
S_n = \(\frac{n}{2}\) (a+l) => S₁₂ = \(\frac{12}{2} (20+120)\) = 6*140 = 840.

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