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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 123. (page 1185)

In your own words, explain how to determine whether a sequence is an arithmetic.

Short Answer

Expert verified

We have to find the common difference between consecutive terms.

Step by step solution

01

Step 1. Introduction of sequence.

Consider that there is a sequence that is defined as:

$a_{1} + a_{2} + a_{3} + \dots + a_{n}$

Let's consider that the above sequence is an arithmetic sequence.

02

Step 2. Explanation.

According to step 1, the sequence is an arithmetic sequence. So, the common difference of consecutive will be the same.

$\begin{array}{rcl} a_{2} - a_{1} & = & d \\ a_{3} - a_{2} & = & d \\ a_{n} - a_{n - 1} & = & d \end{array}$

Thus, by finding the common difference, we can identify whether the given sequence is an arithmetic sequence or not.

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Most popular questions from this chapter

Find the sum of the first $20$ terms of the geometric sequence $3, 6, 12, 24, 48, 96, \dots$ .

The expansion is $y^{5} + 10 y^{4} + 40 y^{3} + 80 y^{2} + 80 y + 32$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = 27$ and $r = \frac{1}{3}$

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find $a_{13}$ given $a_{1} = 7$ and $r = 2$ .

In the following exercises, evaluate.

(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

See all solutions

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