Find number of triplets of integers which are in arithmetic progression and sum of whose squares is `1994.`

Find three consecutive terms in an arithmetic progression whose sum is 18 and sum of their square is 140.

The sum of the first three terms of an arithmetic progression is 9 and the sum of their squares is 35. The sum of the first n terms of the series can be

The sum of the first three terms of an arithmetic progression is 9 and the sum of their squares is 35. The sum of the first n terms of the series can be

The sum of the first three terms of the arithmetic progression is 30 and the sum of the squares of the first term and the second term of the same progression is 116. Find the seventh term of the progression if its fith term is known to be exactly divisible by 14.

Find the consecutive positive integers, sum of whose squares is 145.

Find two negative integers whose difference is 3 and sum of their squares is 89.

If the sum of the first 100 terms of an arithmetic progression is -1 and the sum of the even terms is 1, then the 100^("th") term of the arithmetic progression is

If the sum of the first 100 terms of an arithmetic progression is -1 and the sum of the even terms is 1, then the 100^("th") term of the arithmetic progression is

The sum of the three terms which are in an Arithmetic Progression is 33. if the product of the first and the third terms exceeds the second term by 29, find the Arithmetic Progression.