Q29 of 46 Page 1

The sum of the first 15 terms of an AP is 750 and its first term is 15. Find its 20th term.

Given: Sum of first 15 terms of an AP is 750 and first term of the series (a) = 15

⇒ S15 = 750 …(i)


Since,


∴, [∵, a = 15 and n = 15]


⇒ S15 = (7.5)[30 + 14d] = 225 + 105d = 750 [∵, from equation (i)]


⇒ 225 + 105d = 750


⇒ 105d = 750 – 225 = 525


⇒ d = 525/105 = 5


We have a = 15 and d = 5 and we have to find a20.


a20 = a + 19d [∵, an = a + (n – 1)d]


⇒ a20 = 15 + 19×5 = 15 + 95 = 110


Thus, its 20th term is 110.


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