Question

if 8th term of an apis 31 and the 15rh term is 16 more than 11th term find the ap

Answer 1

it is given that :

a8 = 31
a + 7d = 31 ----------- eq 1

a15 = 16
a + 14d = 16 ------------ eq 2

by adding eq 1 and 2

a+7d = 31 + a+14d = 16
change the sign.

-7d = 15
d = -15/7

now put this value in an equation you will get the value of a.

a + 7d = 31
a + 7 × -15/7 = 31
a = 31 + 15
a = 46.

a11 = a+10d
= 46 + 10 × -15/7
= 46 - 150/7
= 322 - 150 whole divided by 7
= 172/7.

Answer 2

let d is the common difference and a is the 1st term
8a=a+7d=31
15a=14d+a=11a+16(a+10d)+16
a+10d+16=a+14d
4d=16
d=4

a+7d=31
a+28=31
a=3
d=4
therefore ap= a,a+d,a+2d,a+3d.....
putting values
3,7,11,15....
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