Question

Which term of an $A.P7,3,-1....is-89?$

Answer 1

Find the term of an A.P.

Given:

$A.P7,3,-1,...$

Here:

$\text{First term}a=7,\text{common difference}d=3-7=-4,$ $t_n=-89$

${\mathbf{t}}_{\mathbf{n}}$ $\mathbf{=}\mathbf{a}\mathbf{+}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{d}$

$\Rightarrow -89=7+(n-1)\times -4$

$\Rightarrow -89=7-4n+4$

$\Rightarrow -89=7-4n+4$

$\Rightarrow -4n=-89-11=-100$

$\Rightarrow n=\frac{-100}{4}=25$

$\therefore {25}^{th}$term of an A.P is $-89$

Hence, the ${25}^{th}$term of an A.P is $-89$