Questions

If the third term of an A.S. is 7 and $\rm 7^{th} $ terms exceeds 3 times the third term by 2, find the sum of first 30 terms.

How many terms must be taken of the series$\rm - 16 - 15 - 14 - \dots $ makes the sum -100? Explain the double answer.

How many terms of the series $\rm 42 + 39 + 36 + \dots $ make the sum 315? Explain the double answer.

How many terms are there in A.S. Whose first term and fifth term are -14 and 2 respectively, and the sum of the terms is 40?

How many terms of the series $\rm 24 + 20 + 16 +\dots $ must be taken so that the sum may be 72?

The sum of five numbers in an A.S. is 15 and the sum of their squares is 55. Find the numbers.

Three numbers are in AS. If the sum of these numbers is 27 and the product is 585, find the numbers.

The sum of three numbers in an A.S. is 39 and their product is 2184. Find the numbers

If the first term (a = 1), the last term (b = $\rm 58 \frac {1}{2}$), and the sum is 714, then find the number of terms and common difference.

If the first term (a = 9), the last term (b = -6), and the sum is 24, then find the number of terms and common difference.