Chapter 12: Q. 273 (page 1218)

In the following exercises, find the sum of the first $30$ terms of each arithmetic sequence.
$7, 4, 1, - 2, - 5, . . .$

Short Answer

Expert verified

The sum is equal to $- 1095$ .

Step by step solution

Step 1. Given Information

We are given a sequence $7, 4, 1, - 2, - 5, . . .$

The sum of first thirty term is given by,

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

Step 2. Finding the terms

The first term is $7$ ,

The common difference is given by,

$d = 4 - 7 d = - 3$

The thirty term is given by,

$a_{30} = a + (30 - 1) d a_{30} = 7 + (29) (- 3) a_{30} = 7 - 87 a_{30} = - 80$

Step 3. Finding the sum

Putting the values in formula, we get

$S_{n} = \frac{n}{2} (a + a_{n}) S_{30} = \frac{30}{2} (7 + (- 80)) S_{30} = 15 (7 - 80) S_{30} = 15 (- 73) S_{30} = - 1095$

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In the following exercises, find the sum of the first $30$ terms of each arithmetic sequence.
$7, 4, 1, - 2, - 5, . . .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the terms

Step 3. Finding the sum

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In the following exercises, find the sum of the first 30terms of each arithmetic sequence.7,4,1,−2,−5,...

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the terms

Step 3. Finding the sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Statistics

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.
$7, 4, 1, - 2, - 5, . . .$