Chapter 12: Q 117. (page 1185)

In the following exercises, find each sum.
$\sum_{i = 1}^{40} (8 i - 7)$

Short Answer

Expert verified

The obtained sum is 6280.

Step by step solution

Step 1. Given Information.

Consider the given sum: $\sum_{i = 1}^{40} (8 i - 7)$

simplify the sum.

Express the sum and identify the values.

$\begin{array}{rcl} \sum_{i = 1}^{40} (8 i - 7) & = & (8 (1) - 7) + (8 (2) - 7) + (8 (3) - 7) + \dots + (8 (40) - 7) \\ = & 1 + 9 + 17 + \dots + 313 \\ = & a_{1} + a_{2} + a_{3} + \dots + a_{n} \end{array}$

Step 3. Find the sum.

Substitute the values in some formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ .

$\begin{array}{rcl} S_{40} & = & \frac{40}{2} (1 + 313) \\ = & 20 (314) \\ = & 6280 \end{array}$

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In the following exercises, find each sum.
$\sum_{i = 1}^{40} (8 i - 7)$

Short Answer

Step by step solution

Step 1. Given Information.

simplify the sum.

Step 3. Find the sum.

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In the following exercises, find each sum.∑i=1408i−7

Short Answer

Step by step solution

Step 1. Given Information.

simplify the sum.

Step 3. Find the sum.

One App. One Place for Learning.

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In the following exercises, find each sum.
$\sum_{i = 1}^{40} (8 i - 7)$