Answer with Step-by-step explanation:
The sum of first n terms of an arithmetic progression is given by:
[tex]S(n)=\dfrac{n}{2}\times (A1+An)[/tex]
10+25+40+...+85
Since, the terms have a common difference of 15
So, it is an arithmetic progression of n=6 terms with first term A1=10
and A6=85
We have to find S(6)
[tex]S(6)=\dfrac{6}{2}\times (10+85)[/tex]
= 285
Hence, the sum of the terms of the series 10 + 25 + 40 + . . . + 85 is:
285
