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If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, then what is the AP?

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7, 12, 17, 22

10, 15, 20, 25

6, 8, 10, 12

8, 13, 18, 23

answer is B.

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Detailed Solution

Given that the 10th term of an AP is 52 and 17th term is 20 more than its 13th term. Let first term is a and the common difference is d.
Formula used for nth term of A.P.:

t n = a + n − 1 d

Apply formula of

n t h

term of AP in the first given condition.

t 10 = a + (10 − 1) d ⇒ 52 = a + 9 d -----(1)

Applying formula of

n^{th}

term of AP in the second given condition.

t 17 = 20 + t 13

Apply formula of

n t h

term of AP and calculate 13th term:

∴ t 13 = a + (13 − 1) d ⇒ t 13 = a + 12 d -----(3)

Apply formula of

n t h

term of AP and calculate 17th term:

∴ t 17 = a + (17 − 1) d ⇒ t 17 = a + 16 d ------(4)

Putting the value of

t 17

from equation (3) in equation (2):

∴ a + 16 d = 20 + a + 12 d ⇒ 4 d = 20 ⇒ d = 204 ⇒ d = 5

Putting the value of d in equation (1):

∴ a + 9 × 5 = 52 ⇒ a + 45 = 52 ⇒ a = 52 − 45 ⇒ a = 7

Putting the value of a and d in the general series:

∴ (7), [7 + 5], [7 + 2 × 5], [7 + 3 × 5], … … ⇒ (7), (12), (7 + 10), (7 + 15), … … ⇒ (7), (12), (17), (22), …

Therefore, AP series is 7,12,17,22.
Hence, option (2) is correct.

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