Chapter 12: Q 110. (page 1185)

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
16, 10, 4, −2, −8, …

Short Answer

Expert verified

The obtained sum is -2130.

Step by step solution

Step 1. Given Information.

The arithmetic sequence is $16, 10, 4, - 2, - 8, \dots$ .

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl} d & = & 10 - 16 \\ = & - 6 \end{array}$

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

$\begin{array}{rcl} a_{30} & = & 16 + (30 - 1) (- 6) \\ = & 16 - 174 \\ = & - 158 \end{array}$

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.

$\begin{array}{rcl} S_{30} & = & \frac{30}{2} (16 - 158) \\ = & 15 (- 142) \\ = & - 2130 \end{array}$

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In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
16, 10, 4, −2, −8, …

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Find the common difference d.

Step 3. Use the sum formula.

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In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.16, 10, 4, −2, −8, …

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

Geometry

Decision Maths

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.
16, 10, 4, −2, −8, …