Question

Write the series 7 + 10 + 13 + 16 using sigma notation.

Short answer

The sigma notation for the series is$\sum _{n=1}^4(3n+4)$ .

Step-by-step solution

Step 1. Given Information.

Given series is 7 + 10 + 13 + 16.

Step 2. Calculation.

Here, the common difference is $10-7=3$

The nth term of the sequence is given by

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=7+(n-1)\left(3\right)\\ a_n=7+3n-3\\ a_n=3n+4\end{array}$

Since there are four terms i.e. n goes from 1 to 4, the summation is given by:$\sum _{n=1}^4(3n+4)$

Step 3. Conclusion.

Hence, the sigma notation is $\sum _{n=1}^4(3n+4)$.