Chapter 11: Q8. (page 586)

Find the sum of each arithmetic series.
$5 + 11 + 17 + ... + 95$

Short Answer

Expert verified

The sum of the arithmetic series is800.

Step by step solution

Step 1. Given Information.

Given arithmetic series is $5 + 11 + 17 + ... + 95$ .

Step 2. Calculation.

The difference between the terms is $11 - 5 = 6$

The nth term of an arithmetic series is given by $a_{n} = a_{1} + (n - 1) d$

Here, $a_{1} = 5, d = 6, a_{n} = 95$

Plugging the values:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 95 = 5 + (n - 1) (6) \\ (n - 1) (6) = 95 - 5 \\ (n - 1) (6) = 90 \\ n - 1 = 15 \\ n = 15 + 1 \\ n = 16 \end{array}$

The sum $S_{n}$ of the first n terms of an arithmetic series is given by

$S_{n} = \frac{n}{2} (a_{1} + a_{n})$

Here, $a_{1} = 5, n = 16, a_{n} = 95$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (a_{1} + a_{n}) \\ S_{16} = \frac{16}{2} (5 + 95) \\ S_{16} = 8 (100) \\ S_{16} = 800 \end{array}$

Step 3. Conclusion.

Hence, the sum is 800.

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Find the sum of each arithmetic series.
$5 + 11 + 17 + ... + 95$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the sum of each arithmetic series.5+11+17+...+95

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Geometry

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the sum of each arithmetic series.
$5 + 11 + 17 + ... + 95$