Question

determine the AP whose third term is 15 and seventh term is 23​

Answer 1

Hi , your answer is A.P = 11 , 13 , 15 , 17 , ...

Step-by-step explanation:

Given:

a3 = 15

a7 = 23

____________

Let's expand these equations :

an = a + (n-1)d

a3 = a +(3-1)d = 15

a7 = a + (7-1)d = 23

_______________

a +(2)d = 15______(1)

a + (6)d = 23_____(2)

____________

Let's solve these equations (1) & (2) using elimination method.

a +2d = 15______(1)

- a +6d = 23_____(2)

(-4)d = (-8)

-4d= -8

d=(-8)/(-4)

d=8/4

d=2__(3)

Substituting (3) in (1),

a+2(2)=15

a+4=15

a=15-4

a=11

We found both a & d . From these we can find the A.P :

a1 =11

a2 = a+d = 13

a3 = a+2d = 15

a4 = a+3d = 17

& so on...

A.P = 11,13,15,17,...

Hope it's clear !