What is the sum of the first 51 terms of an AP whose second and third terms are 14 and 18 respectively?

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5610

5000

5500

5550

answer is A.

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Detailed Solution

Given that the second and third term are 14 and 18 respectively.
Let the first term be a and the common difference be d.
Determining common difference:

∴ d = a 3 − a 2 ⇒ d = 18 − 14 ⇒ d = 4

Formula used for nth term of A.P.:

a n = a + n − 1 d

Determining first term:

∴ a n = a + (n − 1) d ⇒ a 2 = a + (2 − 1) 4 ⇒ 14 = a + 4 ⇒ a = 14 − 4 ⇒ a = 10

Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Determining the sum of 51 terms:

∴ S 51 = 512 [2 × 10 + (51 − 1) 4] ⇒ S 51 = 512 [20 + (50) 4] = 512 [20 + 200] = 512 [220]

⇒ S 51 = 5610

Therefore, the sum of 51 terms is 5610.
Hence, option (1) is correct.

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