Question

The ${11}^{th}$ term and the ${21}^{st}$ term of an A.P. are $16$ and $29$ respectively, then find the first term and common difference.

Answer 1

Given, $t_{11}=16$ and $t_{21}=29$.
We know that, $t_n=a+(n-1)d$
$\therefore t_{11}=a+(11-1)d$
and $t_{21}=a+(21-1)d$
$\therefore 16=a+10d...\left(i\right)$
and $29=a+20d...\left(ii\right)$
Subtracting equation (i) from (ii), we get
$10d=13\Rightarrow d=1.3$
Putting the value of $d$ in equation (i), we get
$16=a+10\left(1.3\right)\Rightarrow a=3$.