Question

If 18 terms are inserted between 4 and 60 such that the resulting sequence is an AP, then find the sum of resulting AP.

Answer 1

If we insert 18 terms in between 4 and 60, the total number of terms, $n$, will be equal to 20.
Also, $a_1=4$ and $a_{20}=60$
Moreover, we know that the sum to $n$ terms of the AP is given by
$S_n=\frac{n}{2}(a+l),$ where $a$ and $l$ are the first and last terms of the AP respectively. $\left[1mark\right]$

$\therefore S_{20}=\frac{20}{2}(4+60)=10\left(64\right)=640$ $\left[1mark\right]$