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.

The nth term of a progression is (3n + 5). Prove that this progression

1.	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» 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.