IXL - Identify arithmetic and geometric series (Precalculus practice)

Classify the series.

arithmetic

geometric

both

neither

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question

Classify the series.

arithmetic

geometric

both

neither

key idea

A sequence is an ordered list of numbers. This list can have a finite number of terms or infinitely many terms.

A series is a sum of a sequence of numbers.

A series is arithmetic if the differences between consecutive terms are all the same.

–

A series is geometric if the ratios between consecutive terms are all the same.

solution

Find the first few terms of the series. Plug values of

into the expression

starting with the lower limit,

(The last term is also shown.)

248

Now look at the consecutive differences and the consecutive ratios among the first few terms.

n	4 n	a n + 1 – a n	a n + 1 a n
1	4	4	2
2	8	4	3 2
3	12	4	4 3
4	16	4	5 4
5	20	4	6 5

The consecutive ratios are not all equal, so the series is not geometric.

The consecutive differences of the first few terms are the same. To verify this for all terms, look at the difference

–

for an arbitrary index

–

[

(

)

]

–

For all values of

–

So, the series is arithmetic.

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Not feeling ready yet? These can help:

MM.6Write a formula for an arithmetic sequence

MM.7Write a formula for a geometric sequence

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