Chapter 11: Q6. (page 586)

Find $S_{n}$ for each arithmetic series described.
localid="1648548029213" $a_{1} = 132, d = - 4, a_{n} = 52$

Short Answer

Expert verified

$S_{n}$ for the arithmetic series is $S_{21} = 1932$ .

Step by step solution

Step 1. Given Information.

Given arithmetic series is $a_{1} = 132, d = - 4, a_{n} = 52$ .

Step 2. Calculation.

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

Here, $a_{1} = 132, d = - 4, a_{n} = 52$ $a_{1} = 132, d = - 4, a_{n} = 52$

Plugging the values:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 52 = 132 + (n - 1) (- 4) \\ 52 - 132 = (n - 1) (- 4) \\ (n - 1) (- 4) = - 80 \\ n - 1 = 20 \\ n = 20 + 1 \\ n = 21 \end{array}$

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

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

Here, $a_{1} = 132, n = 21, d = - 4$ $a_{1} = 132, n = 21, d = - 4$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d) \\ S_{21} = \frac{21}{2} (2 (132) + (21 - 1) (- 4)) \\ S_{21} = \frac{21}{2} (264 + (20) (- 4)) \\ S_{21} = \frac{21}{2} (264 - 80) \\ S_{21} = \frac{21}{2} (184) \\ S_{21} = 21 (92) \\ S_{21} = 1932 \end{array}$

Step 3. Conclusion.

Hence, the sum is $S_{21} = 1932$ .

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Find $S_{n}$ for each arithmetic series described.
localid="1648548029213" $a_{1} = 132, d = - 4, a_{n} = 52$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find Sn for each arithmetic series described.localid="1648548029213" a1=132,d=−4,an=52

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

Statistics

Calculus

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find $S_{n}$ for each arithmetic series described.
localid="1648548029213" $a_{1} = 132, d = - 4, a_{n} = 52$