Q19 of 47 Page 1

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find its 20th term.

Given: Sum of first 14 terms = S14 = 1050

And first term = a = 10


We have to find a20.


We know that Sum of n terms, Sn =


⇒ So, S14 =


⇒ 7[20 + 13d] = 1050


⇒ 20 + 13d = 1050/7


⇒ 20 + 13d = 150


⇒ 13d = 150 – 20 = 130


⇒ d = 130/13


∴ d = 10


We know that the nth term or the general term of an A.P is an = a + (n – 1) d where a = first term; n = number of terms and d = common difference.


Now, a20 = 10 + (20 – 1) 10


⇒ a20 = 10 + 19(10)


∴ a20 = 200


Answer: The 20th term is 200.


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