Question

18 terms are inserted between 3 and 45 such that the resulting sequence is an AP. The sum of the resulting (finite) AP including the terms 3 and 45 is ___.

Answer 1

Including the terms 3 and 45, the number of terms in the AP will be 20
Now in the AP, the first term will be 3 and the last term will be 45 and the sum of n terms is $S_n=\frac{n}{2}(firstterm+lastterm)$.
The value of first term(a) = 3, last term(l) = 45 and number of terms(n) = 20.
$S_{20}=\frac{20}{2}(3+45)=10\left(48\right)=480$