ADDING A SERIES OF NUMBERS HAVING A COMMON RATIO

# ADDING A SERIES OF NUMBERS HAVING A COMMON RATIO

Rule: Multiply the ratio by itself as many times as there are numbers in the series. Subtract 1
from the product and multiply by the first number in the series. Divide the result by one less than the ratio.

This rule is best applied when the common ratio is a small number or when there are few numbers in the series. If there are many numbers and the ratio is large, the necessity of multiplying the ratio by itself many times diminishes the ease with which this short cut can be applied. But suppose we are given the series:

53, 106, 212, 424

Here each term is twice the preceding term, and there are four terms in the series. The ratio, 2, is therefore multiplied four times.

2 X 2 X 2 X 2 = 16

Subtract 1 and multiply by the first number.

16 – 1 = 15; 15 x 53 = 795

The next step is to divide by one less than the ratio; however, since the ratio is 2, we need divide only by 1. Thus the sum of our series is

53 + 1 06 + 212 + 424 795 Answer