Question

If $t_{54}$ of an A.P. is $-61$ and $t_4=64,$ find $t_{10}.$

Answer 1

Let $a$ be the first term and $d$ be the common difference
so $t_{54}=a+53d=-61$ (i)
and $t_4=a+3d=64$ (ii)
equation (i) $-$ (ii),
$\Rightarrow$ $50d=-125$
$⟹d=-\frac{5}{2}$

On putting value of $d$ in equation (ii)

$⟹a-\frac{3\times 5}{2}=64$

$⟹a=64+\frac{15}{2}$
$\Rightarrow$ $a=\frac{143}{2}$
so, $t_{10}=a+9d$

$⟹t_{10}=\frac{143}{2}+9(-\frac{5}{2})=49$