Question

The $1^{st}$ term of an A.P. is $-54$ and sixteenth term is $21$. Find the ${12}^{th}$ term.

Answer 1

$a=-54\left\{Given\right\}$

$a_{16}=21\left\{Given\right\}$

$\Rightarrow a+15d=21\{\because a_n=a+(n-1)d\}$

$\Rightarrow -54+15d=21\{\because a=-54\}$

$\Rightarrow 15d=21+54$

$\Rightarrow d=\frac{75}{15}=5$

$\therefore a_{12}=a+11d$

$\Rightarrow =-54+(11\times 5)$

$\Rightarrow =-54+55$

$\Rightarrow a_{12}=1$

Hence the ${12}^{th}$ term is 1.