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Chapter 5: Problem 111

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Short Answer

Expert verified
The given sequence is arithmetic, and the next two terms are -49 and -63.

Step by step solution

01

Determine the Type of the Sequence

The identification of the sequence type, arithmetic or geometric, is based on the difference or ratio between the terms. For arithmetic sequence, the difference between successive terms is constant, whereas for geometric sequence, the ratio of successive terms is constant. Thus, check if the differences or ratios in the given sequence \(7,-7,-21,-35, \ldots\) are constant.
02

Identify an Arithmetic Sequence

Calculate the differences between the consecutive terms in the sequence, i.e., \(-7 - 7 = -14\), \(-21 - (-7) = -14\), \(-35 - (-21) = -14\). Since the difference between successive terms is constant (\(-14\)), we can conclude that the sequence is arithmetic.
03

Find the Next Two Terms for Arithmetic Sequence

Next, use the constant difference to calculate the next two terms. Add the common difference \(-14\) to the last term of the sequence (\(-35\)) resulting in \(-35 - 14 = -49\), which is the next term. The second next term is \(-49 -14 = -63\). So, the next two terms of the sequence are \(-49\) and \(-63\).

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Most popular questions from this chapter

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