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

Question

Philoid · Accepted Answer

Given, a = 10

S₁₄ = 1505

S₁₄ = [2a + (n – 1) d]

1505 = [2(10) + (14 – 1) d]

1505 = 7 [20 + 13d]

215 = 20 + 13d

13d = 215 – 20

13d = 195

d = 15

Now, a₂₅ = a + (n – 1) d

= 10 + (25 – 1) 15

= 10 + 24 * 15

= 10 + 360 = 370

Hence, value of 25^th term is 370