Q26 of 46 Page 1

Sum of the first 14 terms of an AP is 1505 and its first term is 10. Find its 25th term.

Given: Sum of first 14 terms of an AP is 1505 and first term of the series (a) = 10

⇒ S14 = 1505 …(i)


Since,


∴, [∵, a = 10 and n = 14]


⇒ S14 = 7[20 + 13d] = 140 + 91d = 1505 (from equation (i)]


⇒ 140 + 91d = 1505


⇒ 91d = 1505 – 140 = 1365


⇒ d = 1365/91 = 15


We have a = 10 and d = 15 and we have to find a25.


a25 = a + 24d [∵, an = a + (n – 1)d]


⇒ a25 = 10 + 24×15 = 10 + 360 = 370


Thus, its 25th term is 370.


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