Question

Determine the AP whose 5th term is 15 and sum of its 3rd and 8th term is 34.

Answer 1

Let the 1st term of $A.P$ is $a$

and the difference is $d$

So,

According to question ,

$a+4d=15$ ...................1

$a+2d+a+7d=34$ .....................2

By simplifying eq 2

$2a+10d=34$

$a+5d=17$

$a=17-5d$ ..............3

put the value of a in eq 1

$17-5d+4d=15$

$d=2$

put value of d in eq. 3

$a=17-5\left(2\right)$

$a=17-10$

$a=7$

so,

The $A.P$ will be : $7,9,11,13,15,.............$