Chapter 12: Q 109. (page 1185)

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
8, 5, 2, −1, −4, …

Short Answer

Expert verified

The obtained sum is -1065.

Step by step solution

Step 1. Given Information.

The arithmetic sequence is $8, 5, 2, - 1, - 4, \dots$ .

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl} d & = & 5 - 8 \\ = & - 3 \end{array}$

And, now find the 30th term of the sequence.

$\begin{array}{rcl} a_{30} & = & 8 + (30 - 1) (- 3) \\ = & 8 - 87 \\ = & - 79 \end{array}$

Step 3. Use the sum formula.

Use the sum formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ to find the sum of the thirtieth term.

localid="1645453590666" $\begin{array}{rcl} S_{30} & = & \frac{30}{2} (8 - 79) \\ = & 15 (- 71) \\ = & - 1065 \end{array}$

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.

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
8, 5, 2, −1, −4, …

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the common difference d.

Step 3. Use the sum formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Calculus

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence. 8, 5, 2, −1, −4, …

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the common difference d.

Step 3. Use the sum formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Calculus

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
8, 5, 2, −1, −4, …