Question

Find the first 3 terms of an ap if a+a5=22 and a8-a5=6

Answer 1

Answer:

The first three terms of the AP is 7, 9, 11

Step-by-step explanation:

Given,

$a + a_{5} = 22 \\ \\ a + a + 4d = 22 \\ \\ 2a + 4d = 22 \\ \\ 2(a + 2d) = 2(11) \\ \\ a + 2d = 11 \\ \\ \bf a = 11 - 2d \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(i)$

Also,

$a_{8} - a_{5} = 6 \\ \\ a + 7d - (a + 4d) = 6 \\ \\ a + 7d - a - 4d = 6 \\ \\ 3d = 6 \\ \\ \bf d = 2$

Putting the value of d in equation (i) we get :

a = 11 - 2(2)

a = 11 - 4

a = 7

So,

The first three terms of this AP is 7, 7 + 2, 9 + 2, i.e., 7, 9, 11