Q. 164.5( 41 Votes )

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

Answer :

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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