# If the sum to first n terms of an A.P. is , find its 25th term.

Taking n = 1, we get

S1 = 4

a1 = 4

Taking n = 2, we get

S2 = 11

a2 = S2 – S1 = 11 – 4 = 7

Taking n = 3, we get

S3 = 21

a3 = S3 – S2 = 21 – 11 = 10

So, a = 4,

d = a2 – a1 = 7 – 4 = 3

Now, we have to find the 25th term

an = a + (n – 1)d

a25 = 4 + (25 – 1)3

a25 = 4 + 24 × 3

a25 = 4 + 72

a25 = 76

Hence, the 25th term is 76.

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