Question

Find the common ratio and the three terms in the sequence after the last one given.

1) 3,-6,12,-24
2) -1,-5,-25,-125
3) 9,-3,1,-1/3
4) -5, -5/2, -5/4, -5/8

Answer 1

1. -2; 48, -96, 192
2. 5; -625, -3125, -15625
3. -1/3; 1/9, -1/27, 1/81
4. 1/2; -5/16, -5/32, -5/64

Explanation:

If there is a common ratio it can be found by dividing any term by the one before it.

1. The common ratio is -6/3 = -2.

The following three terms can be found by multiplying the last given term by this number, then repeating that process two more times.

The next three terms are (-24)(-2) = 48; (48)(-2) = -96; (-96)(-2) = 192

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2. The common ratio is -5/-1 = 5

3. The common ratio is -3/9 = -1/3

4. The common ratio is (-5/2)/(-5) = 1/2

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Note that the signs of the terms of the sequence alternate when the common ratio is negative.