Problem 31 - College Algebra

Question

Find each indicated sum. $$\sum_{i=1}^{4} 2 i^{2}$$

Step-by-Step Solution

Answer

The sum of the sequence is 60.

Step 1: Identify the Sequence

The given series is \(2 i^{2}\) for \(i\) ranging from 1 to 4. Therefore, the individual terms of the series can be found by substituting \(i\) with each of the integers from 1 to 4 into the sequence \(2 i^{2}\).

Step 2: Find the Individual Terms

Substituting \(i = 1, 2, 3, 4\) into the sequence gives us the terms \(2 \cdot 1^{2}, 2 \cdot 2^{2}, 2 \cdot 3^{2}, 2 \cdot 4^{2}\), which simplifies to 2, 8, 18, and 32, respectively.

Step 3: Sum the Terms

Now, sum the four individual terms: \(2 + 8 + 18 + 32 = 60\).