Question

The nth term of a pattern is 2n+1 . Is the pattern of numbers , so formed , in AP . If so, find its 12th term

Answer 1

$a_n =2n+1\\a_1=2(1)+1=3\\a_2=2(2)+1=5\\a_3=2(3)+1=7\\\\a_2-a_1=2=a_3-a_2$

Hence, this pattern forms a A.P.

$a_1_2=2(12)+1\\a_1_2=24+1=25$

12th term of the A.P. is 25.