Sum of the first

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 [∵, a_n = a + (n – 1)d]

⇒ a₂₅ = 10 + 24×15 = 10 + 360 = 370

Thus, its 25^th term is 370.