Question

question
which of the following is the correct expression for the sum below?
\\(\sum_{k = 2}^{6}(5k + 1)\\)
select the correct answer below:
\\(16+21+\ldots+31\\)
\\(11 + 16+\ldots+31\\)
\\(11 + 16+\ldots+26\\)
\\(6+11+\ldots+31\\)
\\(16+21+\ldots+26\\)

Explanation:

Step1: Find the first - term

When $k = 2$, substitute into $5k + 1$.
$5\times2+1=10 + 1=16$

Step2: Find the last - term

When $k = 6$, substitute into $5k + 1$.
$5\times6+1=30 + 1=31$

Step3: Determine the sum form

The sum $\sum_{k = 2}^{6}(5k + 1)$ is the sum of the terms where the first term is 16 and the last term is 31 with a common difference of 5 (since the expression is linear in $k$), so it is $16 + 21+\cdots+31$.

Answer:

A. $16 + 21+\cdots+31$