Question

the 8th term of an ap is equal to 3 times its third term if its sixth term is 22 find the AP

Answer 1

a6=22
a+5d=22
a=22-5d
a8=3(a3)
a+7d=3(a+2d)
a+7d=3a+6d
22-5d+7d=3(22-5d)+6d
22+2d=66-15d+6d
-44=-11d
d=4
a=22-5*4
22-20 = 2
ap is 2,6,10....

Answer 2

Heya!

Here is yr answer.....

Given,

8th term of an AP is equal to 3 times its third term

Its sixth term is 22

Now,

a3 = a+2d

a8 = 3(a+2d)

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

a+7d = 3a+6d

a-3a = 6d-7d

-2a = -d

d = 2a

a6 = a+5d =22

a = 22-5d

d = 2(22-5d)

d = 44-10d

d+10d = 44

11d = 44

d = 44/11

d = 4

______________

a+5d = 22

a+5(4) = 22

a+20= 22

a = 22-20

a = 2

_________________



a2 = a+d

a2 = 2+4

a2 = 6

________________

a3 = a+2d

a3 = 2+2(4)

a3 = 2+8

a3 = 10

_________________

a4 = a+3d

a4 = 2+3(4)

a4 = 2+12

a4 = 14

_________________

a5 = a+4d

a5 = 2+4(4)

a5 = 2+16

a5 = 18

__________________

a7 = a+6d

a7 = 2+6(4)

a7 = 2+24

a7 = 26

__________________

a8 = a+7d

a8 = 2+7(4)

a8 = 2+28

a8 = 30

__________________



AP --------

2 , 6 , 10 , 14 , 18 , 22 , 26 , 30.......


Hope it hlpz....