Question

if the 8th term of an A.P is 31 and it's 15th term is 16 more than the 11th term, find the A.P.

Answer 1

since A.P series is like this

a, (a+d), (a+2d), (a+3d), (a+4d), ……………………………. , {a+(n-1)d}

and nth term is given by = {a+(n-1)d}

so 8th term will be a+7d ,

11th term will be a+10d and

15th term will be a+14d

so as per qn.

a+7d= 31 ……………… (1)

& a+14d = a+10d +16

therefore 4d = 16

& d = 4 ……………….. (2)

use by using (2) in (1)

a + 7 *4 = 31

we get a = 31–28 = 3

so the required A.P will be 3, 7, 11, 15, 19, 23, ……………………

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