Question

Prove that square of any term of the sequence 1, 4, 7, 10,... is also the term of the sequence​

Answer 1

Given sequence is 1, 4, 7,10.

a1 = 1, a2 = 4,  a3  = 7 , a4 = 10.

We  see that a2 -a1 = 4-1 =3. , a3-a2 = 7-4 = 3, a4 - a3 = 10-7 = 3.

Therefore the successive terms have the same  difference or common difference d = 3.

The starting term is a1 = 1.

Therefore the n th term , an = a1 + (n-1)d = 1+(n-1)3.

So an = 1+(n-1)3 =  1+3n-3 = 3n-2.

Therefore the nth term an = 3n-2