Chapter 12: Q 118. (page 1185)

In the following exercises, find each sum.
$\sum_{i = 1}^{45} (7 i - 5)$

Short Answer

Expert verified

The obtained sum is 7020.

Step by step solution

Step 1. Given Information.

Consider the given sum: $\sum_{i = 1}^{45} (7 i - 5)$

simplify the sum.

Express the sum and identify the values.

$\begin{array}{rcl} \sum_{i = 1}^{45} (7 i - 5) & = & (7 (1) - 5) + (7 (2) - 5) + (7 (2) - 5) + \dots + (7 (45) - 5) \\ = & 2 + 9 + 16 + \dots + 310 \\ = & a_{1} + a_{2} + a_{3} + \dots + a_{n} \end{array}$

Step 3. Find the sum.

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

$\begin{array}{rcl} S_{45} & = & \frac{45}{2} (2 + 310) \\ = & \frac{45}{2} (312) \\ = & 45 (156) \\ = & 7020 \end{array}$

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In the following exercises, find each sum.
$\sum_{i = 1}^{45} (7 i - 5)$

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=1457i−5

Short Answer

Step by step solution

Step 1. Given Information.

simplify the sum.

Step 3. Find the sum.

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, find each sum.
$\sum_{i = 1}^{45} (7 i - 5)$