Question

What is the sum of the arithmetic series below? Use the formula for the sum of an arithmetic series.

Answer 1

To determine the sum of the arithmetic series, simply remember that i is the pattern that you are going by which is 1,2,3.

The top value on the sigma sign tells you the final value that you must go to.

So use the equation to go from 1 to 18. So it would be 2(1) + 9 + 2(2) + 9 etc.

Answer 2

Answer:  The required sum is 504.

Step-by-step explanation:  We are given to find the sum of the following arithmetic series using the formula for the sum of an arithmetic series :

$\sum_{i=1}^{18}(2i+9).$

The given arithmetic series can be written, in expanded form, as follows :

$11+13+15+17+~.~.~.~+43+45.$

We know that

the sum of first n terms of an arithmetic series with first term a and common difference d is given by

$S=\dfrac{n}{2}\{2a+(n-1)d\}.$

In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.

Therefore, the sum up to 18 terms will be

$S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.$

Thus, the required sum is 504.