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

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 thatthe 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.