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

Given: 10th term of the AP is 52.

17th term is 20 more than the 13th term.

Let the first term be a and the common difference be d.

Since,

an = a + (n - 1) × d

therefore for 10th term, we have,

52 = a + (10 - 1) × d

52 = a + 9d ………… (1)

Now, 17th term is 20 more than the 13th term.

a17 = 20 + a13

a + (17 - 1)d = 20 + a + (13 - 1)d

16d = 20 + 12d

4d = 20

d= 5

from equation (1), we have,

52 = a + 9d

52 = a + 9 × 5

52 = a + 45

a = 52 - 45

a = 7

AP is a, a + d, a + 2d, a + 3d,…

AP is 7, 12, 17, 22….

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