Question

1. Find the AP whose 5th term is 14 and 9th term is 26.​

Answer 1

Answer:

Let the AP have first term = a

and

common difference = d

Now,

Given that 5th term of an AP is 14 i.e.

$a_5 = 14 \\ \\ a + 4d = 14 \: \: \: ....( i)$

And

9th term of the AP is 26

i.e.

$a_9 = 26 \\ \\ a + 8d = 26 \: \: .....(ii)$

solving (i) and (ii) simultaneously we get

a = 2

And

d = 3.

So first term of the AP is 2 and common difference is 3 .

Now,

$a_1 = 2 \\ \\ a_2 = a + d = 5 \\ \\ a_3 = a + 2d = 8 \\ \\a_4 = a + 3d = 11 \\ \\a_5 = a + 4d = 14 \\. \\ . \\ . \\ . \\ . \\ . \\ . \\ . \\ . \\ .$

So,

AP will be

2 , 5 , 8 ,11,14,.........