Question

The given series has six terms. what is the sum of the terms of the series? 10 + 25 + 40 + . . . + 85

Answer 1

10+25+40+55+70+85
           35+95+155
             130+155
                 285

answer: 285
              

Answer 2

Answer with Step-by-step explanation:

The sum of first n terms of an arithmetic progression is given by:

$S(n)=\dfrac{n}{2}\times (A1+An)$

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)

$S(6)=\dfrac{6}{2}\times (10+85)$

             = 285

Hence, the sum of the terms of the series 10 + 25 + 40 + . . . + 85 is:

285