Question

The 9th term of an ap is equal to 7 times its third term and the 13th term is exceeds three times its 5th term by 8. find the 27th term.

Answer 1

Answer:

27th term=100

Explanation:

ATQ

9th term of an ap is equal to 7 times its third term

a+8d=7(a+2d)

a+8d=7a+14d

6a+6d=0

a+d=0- - - 1

also

13th term exceeds three times its 5th term by 8

a+12d=[3(a+4d)]+8

a+12d=3a+12d+8

2a+8=0

a+4=0

a= -4

on putting value of a in 1 we get

a+d=0

-4+d=0

d=4

27th term

=a+26d

=-4+26(4)

=-4+104

=100

Answer 2

Answer:

27th tearm = 100

Explanation:

given,

a1+8d=7(a1+2d) -(1)

a1+12d-3(a1+4d)=8

After solving both the equation. We get,

(a1=-d) -(from1)

(a1=-4) -(from2)

so d=4 and a1=-4

Now,

27th term=a1+26d

=100 ans.