Chapter 11: Q7. (page 586)

Find $S_{n}$ for each arithmetic series described.
$d = 5, n = 16, a_{n} = 72$

Short Answer

Expert verified

$S_{n}$ for the arithmetic series is $S_{16} = 552$ .

Step by step solution

Step 1. Given Information.

Given arithmetic series is $d = 5, n = 16, a_{n} = 72$ .

Step 2. Calculation.

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

Here, $d = 5, n = 16, a_{n} = 72$

Plugging the values:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 72 = a_{1} + (16 - 1) (5) \\ 72 = a_{1} + (15) (5) \\ 72 = a_{1} + 75 \\ a_{1} = 72 - 75 \\ a_{1} = - 3 \end{array}$

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

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

Here, $a_{1} = - 3, n = 16, d = 5$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d) \\ S_{16} = \frac{16}{2} (2 (- 3) + (16 - 1) (5)) \\ S_{16} = 8 (- 6 + (15) (5)) \\ S_{16} = 8 (- 6 + 75) \\ S_{16} = 8 (69) \\ S_{16} = 552 \end{array}$

Step 3. Conclusion.

Hence, the sum is $S_{16} = 552$ $S_{16} = 552$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find $S_{n}$ for each arithmetic series described.
$d = 5, n = 16, a_{n} = 72$

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

Geometry

Pure Maths

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find Snfor each arithmetic series described.d=5,n=16,an=72

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

Geometry

Pure Maths

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find $S_{n}$ for each arithmetic series described.
$d = 5, n = 16, a_{n} = 72$