Answer
$30,919$
Work Step by Step
We have to determine the sum:
$S=73+78+83+.....+558$
As $78-73=83-78=...=5$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=73$
$d=5$
The terms can be written as:
$73=5\cdot 14+3$
$78=5\cdot 15+3$
$83=5\cdot 16+3$
..............................
$558=5\cdot 111+3$
Therefore, the given sum contains $111-13=98$ terms, so we have to determine the sum of the first $98$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$73+78+83+...+558=\dfrac{98(73+558)}{2}$
$=\dfrac{98\cdot 631}{2}$
$=30,919$
