Question

Write the algebraic form of 1,4,7,10,… is 100 a term of this sequence. Why? Prove that the square of any term of this sequence belongs to that sequence.

Answer 1

1,4, 7, 10,…

f = 1, d = 3

x_n = dn + (f – d) = 3n + (1 – 3) = 3n – 2

When 4 is divided by 3 we get remainder as 1 When 100 is divided by 3 we get remainder as 1 

So, 100 is a term of the arithmetic sequence.

Square = (3n – 2)² = 9n² – 12n + 4 (9n² – 12n + 4) + 3

When 9n² – 12n + 4 is divided by 3the remainder is 1. 

So square of the term also in the sequence.

∴ The square of any term of this sequence belongs to that sequence.