Question

The 8th term of an ap is equal to three times it's third term . If it's 6th term is 22,find the ap.

Answer 1

this is the answer. thank you.

Answer 2

Hi !

8th term = a₈ = a + 7d
3rd term = a₃ = a + 2d

given,

a + 7d = 3 ( a + 2d)
a + 7d = 3a + 6d 

2a - d = 0        ----> (1)

----------------------------------------------------

6th term = a₆ = 22

a + 5d = 22          -----> (2)

Multiplying equation (2) with 2 ,

2*(a + 5d = 22) -->  2a + 10d = 44     ---> (3)

Solving equations (3) and (4) :-

   2a + 10d = 44
-  2a - d = 0
----------------------
11d = 44

d = 4


2a - d = 0

2a - 4 = 0

2a = 4

a = 2
------------------------------------------------------------

First term = a = 2
second term = a₂ = a + d = 2 + 4 = 6
third term = a₃ = a + 2d = 2 + 4*2 =  10

The A.P is 2,6,10 ......