Chapter 11: Q5. (page 586)

Find $S_{n}$ for each arithmetic series described.
$a_{1} = 40, n = 20, d = - 3$

Short Answer

Expert verified

$S_{n}$ for the arithmetic series is $S_{20} = 230$ .

Step by step solution

Step 1. Given Information.

Given arithmetic series is $a_{1} = 40, n = 20, d = - 3$ .

Step 2. Calculation.

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, $a_{1} = 40, n = 20, d = - 3$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d) \\ S_{20} = \frac{20}{2} (2 (40) + (20 - 1) (- 3)) \\ S_{20} = 10 (80 + (19) (- 3)) \\ S_{20} = 10 (80 - 57) \\ S_{20} = 10 (23) \\ S_{20} = 230 \end{array}$

Step 3. Conclusion.

Hence, the sum is $S_{20} = 230$ .

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Find $S_{n}$ for each arithmetic series described.
$a_{1} = 40, n = 20, d = - 3$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find Snfor each arithmetic series described.a1=40,n=20,d=−3

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

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Find $S_{n}$ for each arithmetic series described.
$a_{1} = 40, n = 20, d = - 3$