Q. 16 A4.2( 5 Votes )

If the 8th term of an AP is 31 and its 15th term is 16 more than the 11th term, find the AP.

Answer :

Let the first term and common difference of given AP be a and d respectively.


According to question –


8th term of AP = a8 = 31 [Given]


a + (8 – 1)d = 31


a + 7d = 31…..(1)


15th term of AP = a15 = 16 + a11


a + (15 – 1)d = 16 + a + (11 – 1)d


14d = 16 + 10d


4d = 16


d = 4


Substituting the value of d in equation(1), we get –


a = 31 – 7 × 4 = 31 – 28 = 3


Thus, the required AP is 3,7,11,15,…….


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