Question

1. Which is a finite arithmetic sequence?

A {7, 10, 13, 16, 19}
B {20, 10, 5, 2.5, 1.25}
C {100, 10, 1, 0.1,…}
D {2, 4, 6, 8, …}

2. Which sequence has a common ratio of -2?
{-1, 2, -4, 8, -16, …}
{29, 27, 25, 23, 21, …}
{4, -6, 8, -10, 12, …}
{900, -450, 225, -112.5, 56.25, …}

Answer 1

1. A {7, 10, 13, 16, 19}
2. {-1, 2, -4, 8, -16, …} . . . (first choice)

Explanation:

You want to identify the sequence that is ...

1. a finite arithmetic sequence
2. one with a common ratio of -2

1. Finite Arithmetic

A finite sequence will not be ending in "...", because that means the sequence is infinite.

An arithmetic sequence has a common difference. The differences of sequence A are all 3, indicating it is the finite arithmetic sequence.

The difference of sequence B are -10, -5, -2.5, ..., which are all different. This is an exponential sequence with a common ratio of 1/2.

Sequence A {7, 10, 13, 16, 19} is a finite arithmetic sequence.

2. Common ratio of -2

The ratio referred to is the ratio of each term to the one before. If the ratio is negative, the signs of the terms will alternate (eliminating choice B).

The ratios of the offered sequences are ...

(a) 2/-1 = -2

(c) -6/4 = -3/2

(d) -450/900 = -1/2

Sequence (a) {-1, 2, -4, 8, -16, ...} has a common ratio of -2.

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