Q29 of 46 Page 1

Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th term.

Given: Sum of first 20 terms of an AP is -240 and first term of the series (a) = 7

⇒ S20 = -240 …(i)


Since,


∴, [∵, a = 7 and n = 20]


⇒ S20 = (10)[14 + 19d] = 140 + 190d = -240 [from equation (i)]


⇒ 140 + 190d = -240


⇒ 190d = -240 – 140 = -380


⇒ d = -380/190 = -2


We have a = 7 and d = -2 and we have to find a24.


a24 = a + 23d [∵, an = a + (n – 1)d]


⇒ a24 = 7 + 23×(-2) = 7 – 46 = -39


Thus, its 24th term is -39.


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