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

Explanation: A sequence is called arithmetic progression if a

_{n+1}= a

_{n}+ d where a

_{1}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*r^{n}

View Answer

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 = ……. = a

_{1}+ 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

Explanation: From the given A.P., a=3 and d=5-3 =2.

We know, a

_{n}= a + (n-1) d => a

_{12}= a+11d = 3+11*2 = 3+22 = 25.

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

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

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.

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

Explanation: Given, a

_{3}= 6 and a

_{5}= 12.

=> a + 2d = 6 and a + 4d = 12

=> 2d = 6 => d=3.

=> a + 2*3 = 6 => a=0

So, a

_{21}= a + 20 d = 0 + 20*3 = 60.

7. If sum of n terms of an A.P. is n^{2}+5n then find general term.

a) n+1

b) 2n

c) 3n

d) n^{2}+3n

View Answer

Explanation: Given, S

_{n}= n

^{2}+5n

We know, a

_{n}= S

_{n}– S

_{n-1}= (n

^{2}+5n) – ((n-1)

^{2}+5(n-1)) = (n

^{2}+5n) – (n

^{2}+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

Explanation: From the given A.P., a=1 and d=7-1 = 6.

We know, S

_{n}= \(\frac{n}{2} (2a+(n-1)d)\)

S

_{22}= \(\frac{22}{2} (2*1+(22-1)6)\) = 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

Explanation: Given, a=20, a

_{12}= 120, n=12.

S

_{n}= \(\frac{n}{2}\) (a+l) => S

_{12}= \(\frac{12}{2} (20+120)\) = 6*140 = 840.

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