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 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 ne-cessity of multiplying the ratio by itself many times di-minishes the ease with which this short cut can be applied. But suppose we are given the series:
53, 106, 212, 924
Here each term is twice the preceding term, and there are four terms in the series.
The ratio, 2, is therefore multi-plied 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 (Short Cut 27)
The next step is to divide by one less than the ratio: how-ever, since the ratio is 2, we need divide only by 1.
Thus the sum of our series is 53 + 106 + 212 + 424 = 795 Answer