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

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

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

Answer»

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.