Questions: ∑(n=1)^(4)(3 n+2) Sum = □

Transcript text: \[ \sum_{n=1}^{4}(3 n+2) \] Sum $=$ $\square$

Solution

Solution Steps

To solve the given summation problem, we need to evaluate the sum of the expression $3n + 2$ from $n = 1$ to $n = 4$. This involves substituting each value of $n$ into the expression, calculating the result, and then summing these results.

Step 1: Define the Summation

We need to evaluate the summation: \[ \sum_{n=1}^{4}(3n+2) \]

Step 2: Substitute Values of $ n $

Substitute $ n = 1, 2, 3, 4 $ into the expression $ 3n + 2 $: \[ \begin{align_} \text{For } n = 1: & \quad 3(1) + 2 = 3 + 2 = 5 \\ \text{For } n = 2: & \quad 3(2) + 2 = 6 + 2 = 8 \\ \text{For } n = 3: & \quad 3(3) + 2 = 9 + 2 = 11 \\ \text{For } n = 4: & \quad 3(4) + 2 = 12 + 2 = 14 \\ \end{align_} \]

Step 3: Sum the Results

Add the results from each substitution: \[ 5 + 8 + 11 + 14 = 38 \]