Question

State whether the following sequence is an A.P. or not?

1, 4, 7, 10, ………………..

Answer 1

1, 4, 7, 10, ……
Let ‘d’ be the common difference, ‘a’ be the common ratio, and t₂ , t₃, t₄ be the 2nd, 3rd
and 4th term respectively.
Here t₂ = 4, t₃ = 7, t₄ = 10
d = 4 – 1 = 3
a = 1
We know t₂ – a = t₃ − t₂ = 3
Since the common difference is same throughout the series, therefore the series is an
A.P.