Question

Can you assist me with the correct arithmetic series sum? See attached pic.

Answer 1

Step-by-step explanation:

The arithmetic series is given below as

`\sum_{k\mathop{=}0}^(18)2k+7`

Step 1:

Figure out the first term and the second term

`\begin{gathered} k=1 \\ 2k+7=2(1)+7=9 \\ k=2 \\ 2k+7=2(2)+7=11 \end{gathered}`

Step 2:

Calculate the common difference

`\begin{gathered} d=t_2-t_1 \\ d=11-9 \\ d=2 \end{gathered}`

Step 3:

Calculate the sum of the arithmetic series using the formula below

`\begin{gathered} S_n=(n)/(2)(2a+(n-1)d) \\ where, \\ n=18 \\ a=9 \\ d=2 \end{gathered}`

By substituting the values, we will have