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.
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.
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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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