Question

The nth term of a progression is (3n + 5). Prove that this progression is an arithmetic progression. Also find its 6th term.
(b) The nth term of a progression is (3 - 4n). Prove that this progression is an arithmetic progression. Also find its common difference.
(c) The nth term of a progression is `(n^(2) - n + 1).` Prove that it is not an A.P.

Answer 1

Here, `a_(n)=3n+5`
`rArr a_(n-1)=3(n-1)+5`
`=3n-3+5=3n+2`
Now, `a_(n)-a_(n-1)=(3n+5)-(3n+2)=3`
Which does not depend on n i.e., it is constant.
`:.` Given sequence is in A.P. `" "` Hence Proved.