Question

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

• A. 59
• B. 49
• C. 36
• D. 64

Answer 1

The correct option is A 59

$t_{54}=a+53d=-\mathrm{64...........}\left(1\right)$
$t_4=a+3d=\mathrm{61.........}\left(2\right)$
Subtracting eq 1 and 2
$50d=-125$
$d=-2.5$
Substitute the value of d in eq 2
$a=64-(3\times -2.5)$
$a=64+7.5=71.5$
$t_{10}=a+9d$
$\Rightarrow 71.5+(9\times -2.5)$
$\Rightarrow 71.5-22.5=49$