Question

The n^th term of a sequence is 8 – 5n. Show that the sequence is an A.P.

Answer 1

t_n = 8 – 5n

Replacing n by (n + 1), we get

t_n+1 = 8 – 5(n + 1)

= 8 – 5n – 5

= 3 – 5n

Now,

t_n+1 – t_n = (3 – 5n) – (8 – 5n) = –5

Since, (t_n+1 – t_n) is independent of n and is therefore a constant.

Hence, the given sequence is an A.P.