Question

The ${54}^{th}$ and $4^{th}$ terms of an A.P. are $-61$ and $64$ respectively. Find the ${23}^{rd}$ term.

• A. $\frac{35}{2}$
• B. $\frac{33}{2}$
• C. $\frac{37}{2}$
• D. $\frac{39}{2}$

Answer 1

The correct option is B $\frac{33}{2}$

Here we use the formula for nth term of an AP: $a_n=a+(n-1)d$

So we have $a+53d=-61....\left(1\right)$
& $a+3d=64....\left(2\right)$
$50d=-125$ [Subtracting $\left(2\right)$ from $\left(1\right)$]
$d=\frac{-5}{2},$ using this value in $\left(2\right)$

$⟹a=64-3d=64+\frac{15}{2}=\frac{143}{2}$
$a_{23}=\frac{143}{2}-22\times \frac{5}{2}=\frac{33}{2}$.