## Find the first term and common difference for each of the A.P.

(1) 5, 1, – 3, – 7, . . . Solution:Given 5, 1, – 3, – 7, . . .First term a1 = 5Second term a2 = 1Third term a3 = – 3We know that d = an + 1 – anThus, d = a2 – a1 = 1 – 5 = – 4Hence, the common difference d = – 4 […]

## Write an A.P. whose first term is a and common difference is d in each of the following.

(1) a = 10, d = 5 Solution:Given a = 10, d = 5Let a1 = a = 10Since, the common difference d = 5Using formula an + 1 = an + dThus, a2 = a1 + d = 10 + 5 = 15a3 = a2 + d = 15 + 5 = 20a4 = a3 + d = 20 + 5 = 25Hence, […]

## Which of the following sequences are A.P.? If they are A.P. find the common difference.

Given 2, 4, 6, 8, . . . Here, the first term, a1 = 2Second term, a2 = 4And a3 = 6Now, common difference = a2 – a1 = 4 – 2 = 2Also, a3 – a2 = 6 – 4 = 2Since, the common difference is same.Hence the terms are in Arithmetic progression with common difference, d = 2. (2) 2, […]