Question

Assume the series 10+18+26... continues for 200 terms. What is the sum?

Answer 1

`a_2-a_1=18-10=8`
`a_3-a_2=26-18=8`

`implies` This is an arithmetic series .

`implies` common difference`=d=8`
first term`=a_1=10`

The sum of arithmetic series is given by

`Sum=n/2{2a_1+(n-1)d}`

Where `n` is the number of terms, `a_1` is the first term and `d` is the common difference.

Here `a_1=10`, `d=8` and `n=200`

`implies Sum=200/2{2*10+(200-1)8}=100(20+199*8)=100(20+1592)=100*1612=161200`

Hence the sum is`161200`.