Question

The $n^{th}$ term of a pattern of number is $(2n+1)$. Is the pattern of number, so formed, in $A.P$? If so, find its ${12}^{th}$ term.

Answer 1

Given,

$a_n=2n+1$

$a_1=2\left(1\right)+1=3$

$a_2=2\left(2\right)+1=5$

$a_3=2\left(3\right)+1=7$

and so on,

The A.P. series follows as,

$3,5,7,10,.........$

$a=3$

$d=5-3=2$

$a_{12}=a+(12-1)d$

$=3+(12-1)2$

$=25$