Prove that the sum of any number of terms of the arithmetic sèquence: 16 , 24,32 , .... starting from the first, added. to 9 gives a perfect square.

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.

16 added to the sum of the first few terms of the arithmetic sequence 9,11,13, ........... gave 256 . How many terms were added?

Consider the arithmetic sequence -46,-42,-38,….., How many terms added from first to get the sum zero?

What is the sum of first 40 natural numbers? [(1640 , 820 , 410 , 205)] ii) Whât is the sum of first 40 terms of the arithmetic sequences 6,12,18,.....? iii) The sum of first 40 terms of an arithmetic sequence with common difference 6 , is '5120 .' Write down the aigebraic form of this sequence.

Consider the arithmetic sequence 16,24,32,…... The sum of the first n consecutive numbers, with which number should be added to get a perfect square number.

Sum of the first 4 terms of an arithmetic sequence is 72. Sum of the first 9 terms is also 72. Write the sequence.

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.

Consider 'the arithmetic sequence 10,17,24,…. i) What is its algebraic form? ii) Prove that there is no perfect square 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 algebraic form for the sum of first n terms of an arithmetic sequence is 2n^(2) +8n'. How many consecutive terms of the sequence, starting from the first, are to be added to get 330 ?