Prove that the squares of the sequence 1,3,5, ... belongs to that sequence itself.

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.

Prove that the squares of all the terms of the arithmetic sequerice 4,7,10,….. belong to the sequence.

Prove that the arithmetic sequence 5,8,11,…... contains no perfect squares.

Consider the arithmetic sequence 17,20,23,26,….. a) Write the algebraic form of this sequence. b) Is 400 a term of this sequence?. c) Is the square of any term of this sequence belongs to this sequence? Why?

Prove that the arithmetic sequence 7,11,15, ………. does not contain perfect square.

Find the n^(th) term of the sequence 3,5,7,………

23,30,37,.... is an arithmetic sequence a) Write the algebraic form of the sequence. b) Write the algebraic form of the sum of n terms of the sequence. c) Prove that the square of any term of this sequence will not be a term in this sequence. d) Prove that there will be so many, perfect squares in this sequence.

Algebraic form of an n^(th) term of an arithmetic sequence is 8n-4. Prove that the sum of the n consecutive terms of this sequence is a perfect square.

The sixth term in the sequence is 3,1, 1/3 ,... is

The sum of first n terms of an arithmetic sequence is n^2+2n Prove that the sum of continuous terms starting from the first of the sequence 3,5,7,..... added to 1 gives a perfect square.