Chapter 12: Q. 276 (page 1218)

In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.
$a_{n} = - 2 n + 19$

Short Answer

Expert verified

The sum is equal to $45$ .

Step by step solution

Step 1. Given Information

We are given general term of a sequence,

$a_{n} = - 2 n + 19$

The sum of first thirty term is given by,

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

Step 2. Finding the terms

Putting $n = 1$ in the general term, we get

$a_{1} = - 2 (1) + 19 a_{1} = - 2 + 19 a_{1} = 17$

The fifteenth term is given by,

$a_{15} = - 2 (15) + 19 a_{15} = - 30 + 19 a_{15} = - 11$

Step 3. Finding the sum

Putting the values in formula, we get

$S_{15} = \frac{15}{2} (17 + (- 11)) S_{15} = \frac{15}{2} (17 - 11) S_{15} = \frac{15}{2} (6) S_{15} = 15 \times 3 S_{15} = 45$

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In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.
$a_{n} = - 2 n + 19$

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.

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In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.an=−2n+19

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

Statistics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.
$a_{n} = - 2 n + 19$