Question

The nth term of a progression is (3 – 4n). Prove that this progression is an arithmetic progression. Also, find its common difference.

Answer 1

Let T_n = 3 − 4n.

`T_((n−1)) = 3 − 4(n−1)`

= 3 − 4n + 4

= 7 − 4n

Now the difference of consecutive terms:

`T_n − T_((n−1))`

= (3 − 4n) − (7 − 4n)

= 3 − 4n − 7 + 4n

= −4