Find the common difference d and the nth term of the arithme

Find the common difference d and the nth term of the arithmetic sequence whose 5th term is 7 and 9th term is 5.

Solution

nth term in AP sequence is

an = a1 + (n - 1)*d

7 = a1 + 6d

and 5 = a1 + 8d

Subtracting both, 2 = -2d ========> d = -1

Also a1 = 13

Then nth term = an = 13 + (n - 1)(-1) = 14 - n