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 :
[tex]\sum_{i=1}^{18}(2i+9).[/tex]
The given arithmetic series can be written, in expanded form, as follows :
[tex]11+13+15+17+~.~.~.~+43+45.[/tex]
We know that
the sum of first n terms of an arithmetic series with first term a and common difference d is given by
[tex]S=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]
In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.
Therefore, the sum up to 18 terms will be
[tex]S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.[/tex]
Thus, the required sum is 504.
