Question

How to find the common difference and the nth term of the arithmetic sequence below? `8, 7 3/4 , 7 1/2, 7 1/4, ....`

Answer 1

The common difference of an arithmetic progression is

`d=a_n-a_(n-1)`

For any `n > 1`.

`d = 7 3/4-8=7 1/2 - 7 3/4=-1/4`

The `n`-th term is given by the formula

`a_n = a_1 + (n-1)d = 8-1/4(n-1)`