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

Here, first term = a = 10

Let the Common difference = d

Sum of first 14 terms = S14 = 1505

Now, Sum of n terms of this arithmetic series is given by:

Sn = [2a + (n - 1)d]

S14 = [2(10) + (14 - 1)d] = 1505

7 × [20 + 13d] = 1505

[20 + 13d] = 215

13d = 195

d = 15

Now, nth term is given by:

an = a + (n - 1)d

a25 = 10 + (25 - 1)15

= 10 + (24 × 15)

= 10 + 360

= 370

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