Question

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

Answer 1

Given,

First term of the A.P is 1505 and

S₁₄ = 1505

We know that, the sum of first n terms is

S_n = \(\frac{n}{2}\)(2a + (n − 1)d)

So,

S₁₄ = \(\frac{14}{2}\)(2(10) + (14 − 1)d) = 1505

7(20 + 13d) = 1505

20 + 13d = 215

13d = 215 – 20

d = \(\frac{195}{13}\)

d =15

Thus, the 25^th term is given by

a₂₅ = 10 + (25 -1)15

= 10 + (24)15

= 10 + 360

= 370

Therefore, the 25^th term of the A.P is 370.