Q. 19 A4.8( 5 Votes )

# If 10th term of an A.P. is 52 and 17th term is 20 more than the 13th term, find the A.P.

Given: a10 = 52 and a17 = 20 + a13

Now, an = a + (n – 1)d

a10 = a + (10 – 1)d

52 = a + 9d …(i)

and a17 = 20 + a13

a + (17 – 1)d = 20 + a + (13 – 1)d

a + 16d = 20 + a + 12d

16d –12d = 20

4d = 20

d = 5

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

a + 9(5) = 52

a + 45 = 52

a = 52 – 45

a = 7

Therefore, the AP is 7, 12, 17, …

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