Question

5th term of an AP is 38 and 8th term is 59.

What is the cd of the sequence?

Which term of the sequence is 185?

Answer 1

Any Nth term of AP can be written as

Tn=a+(n-1)d

Here ,a= first term

n = no of term

d= common difference

Given,

T5=38

T8=59

38=a+(5–1)d

38=a+4d. Eq(1)

59=a+(8–1)d

59=a+7d. Eq(2)

Subtracting (1) and (2)

-21=-3d

d=7
now ,put d=7 in any equation to get a
So put d=7 in equation 1
Therefore,38=a+4(7)
=>a=10
Now to find which term is 185
185=10+(n-1)d
185-10=(n-1)7
175/7=n-1
n=26