RuleMultiply the ratio by itself as many times as there are number of items 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.

In symbol notation:

where:

x = the sum of all numbers in the sries

y = the common ratio of the numbers

a = the first number in the series

n = the number of items in the series

This rule is best applied when the ratio and the number of items in the series are small else the purpose of the short cut will be defeated.

Example:

Add the following numbers: .

Solution:

The traditional way:

RuleAdd the smallest number to the largest number in the series, multiply the sum by the numbers of items in the series, then divide by 2.

where:

– the sum of the numbers in the series

– the smallest number in the series

– the largest number in the series

– the numbers items in the series

Example 1:

Find the sum of the numbers in the series

To calculate the sum of all even numbers in a seires starting from 2, apply the this rule:

RuleMultiply the number of items in the series by the one more than number of items.

In symbol notation:

where:

x = the sum of all odd numbers in the series starting from 2

y = the number of items in the series

To calculate the number of items in a given series, divide the highest number in the series by 2.

Integrating this rule into the above rule.

where N = highest number in the series.

To illustrate this rule, let us have some examples:

Example 1:

Calculate the sume of all odd number from 2 to 48.

Solution:

In this example,

 

Example 2:

Calculate the sume of all odd number from 2 to 86.

Solution:

In this example,

Try the following exercises:

1. 2 to 100 – Answer: 2,550
2. 2 to 124 – Answer: 3,906