Chapter 11: Q13. (page 586)

Find the first three terms of each arithmetic series described.
$n = 8, a_{n} = 36, S_{n} = 120$

Short Answer

Expert verified

The first three terms are-6, 0, 6.

Step by step solution

Step 1. Given Information.

Given arithmetic series is $n = 8, a_{n} = 36, S_{n} = 120$ .

Step 2. Calculation.

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, $n = 8, a_{n} = 36, S_{n} = 120$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (a_{1} + a_{n}) \\ 120 = \frac{8}{2} (a_{1} + 36) \\ 120 = 4 (a_{1} + 36) \\ a_{1} + 36 = 30 \\ a_{1} = 30 - 36 \\ a_{1} = - 6 \end{array}$

The nth term of an arithmetic series is given by

$a_{n} = a_{1} + (n - 1) d$

Here $a_{1} = - 6, a_{n} = 36, n = 8$ $a_{1} = - 6, a_{n} = 36, n = 8$

Plugging the values:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ 36 = - 6 + (8 - 1) d \\ 7 d = 36 + 6 \\ 7 d = 42 \\ d = 6 \end{array}$

Adding the common difference d to a term gives the next term.

Hence,

The second term of the series is $- 6 + 6 = 0$

The third term of the series is $0 + 6 = 6$

Step 3. Conclusion.

Hence, the first three terms are -6, 0, 6.

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Find the first three terms of each arithmetic series described.
$n = 8, a_{n} = 36, S_{n} = 120$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the first three terms of each arithmetic series described.n=8,an=36,Sn=120

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

Decision Maths

Logic and Functions

Applied Mathematics

Statistics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the first three terms of each arithmetic series described.
$n = 8, a_{n} = 36, S_{n} = 120$