Q3. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

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 $\sum _{n=1}^4(3n+4)$ .