Chapter 12: Q 120. (page 1186)

In the following exercises, find each sum.
$\sum_{i = 1}^{25} (4 i + 3)$

Short Answer

Expert verified

The obtained arithmetic sum is 1375.

Step by step solution

Step 1. Given Information.

Consider the given sum:

$\sum_{i = 1}^{25} (4 i + 3)$

simplify the sum.

Express the sum and identify the values.

$\begin{array}{rcl} \sum_{i = 1}^{25} (4 i + 3) & = & (4 (1) + 3) + (4 (2) + 3) + (4 (3) + 3) + \dots + (4 (25) + 3) \\ = & 7 + 11 + 15 + \dots + 103 \\ = & a_{1} + a_{2} + a_{3} + \dots + a_{n} \end{array}$

Step 3. Find the sum.

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

$\begin{array}{rcl} S_{25} & = & \frac{25}{2} (7 + 103) \\ = & \frac{25}{2} (110) \\ = & 25 (55) \\ = & 1375 \end{array}$

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In the following exercises, find each sum.
$\sum_{i = 1}^{25} (4 i + 3)$

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=1254i+3

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

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

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Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find each sum.
$\sum_{i = 1}^{25} (4 i + 3)$