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.

Answer :

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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