Chapter 11: Q9. (page 586)

Find the sum of each arithmetic series.
$38 + 35 + 32 + ... + 2$

Short Answer

Expert verified

The sum of the arithmetic series is260.

Step by step solution

Step 1. Given Information.

Given arithmetic series is $38 + 35 + 32 + ... + 2$ .

Step 2. Calculation.

The difference between the terms is $35 - 38 = - 3$

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

Here, localid="1648547769020" $a_{1} = 38, d = - 3, a_{n} = 2$

Plugging the values:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 2 = 38 + (n - 1) (- 3) \\ (n - 1) (- 3) = 2 - 38 \\ (n - 1) (- 3) = - 36 \\ n - 1 = 12 \\ n = 12 + 1 \\ n = 13 \end{array}$

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

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

Here, localid="1648547799867" $a_{1} = 38, n = 13, a_{n} = 2$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (a_{1} + a_{n}) \\ S_{13} = \frac{13}{2} (38 + 2) \\ S_{13} = \frac{13}{2} (40) \\ S_{13} = 13 (20) \\ S_{13} = 260 \end{array}$

Step 3. Conclusion.

Hence, the sum is 260.

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Find the sum of each arithmetic series.
$38 + 35 + 32 + ... + 2$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the sum of each arithmetic series.38+35+32+...+2

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

Applied Mathematics

Logic and Functions

Decision Maths

Statistics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the sum of each arithmetic series.
$38 + 35 + 32 + ... + 2$