# The 8th term of an A.P. is 37, and its 12th term is 57. Find the A.P.

We have

a8 = a + (8 – 1)d = a + 7d = 37 …(1)

and a12 = a + (12 – 1)d = a + 11d = 57 …(2)

Solving the pair of linear equations (1) and (2), we get

a + 7d – a – 11d = 37 – 57

– 4d = –20

d = 5

Putting the value of d in eq (1), we get

a + 7(5) = 37

a + 35 = 37

a = 2

Hence, the required AP is 2, 7, 12, 17,…

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