How many terms of the A.P. 25, 22, 19, …. are needed to give the sum 116 ? Also find the last term.

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78 ? Explain the double answer.

In an A.P., the 5^th and 9^th terms are 4 and -12 respectively. Find the:

(a) first term

(b) common difference

(c) sum of the first 20 terms.

Find the sum of first 51 terms of the A.P. whose second and third terms are 14 and 18 respectively.