The skill is in

- Identifying patterns
- Taking a sample and deriving meaning full relationships between the various elements in the pattern
- Expostulating the pattern to encompass the entire series
- Use this new knowledge to arrive at an answer

*The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then what is the value of n?*

This sum involves a set of even numbers from 1 to n.(n is an odd number)

Lets derive the pattern

First let n =5

Then the even numbers involved are 2,4

Hence, Sum = 2+4 = 6

6 can be written as 2 *3( Same pattern as 79*80)

Now let n =7

The even numbers are 2,4,6

Sum = 2+4+6 = 12 i.e 3*4

So you get a pattern 2*3, 3*4…………………….79*80, when n = 5,7……n

Do you observe that 2+3 =5 and 4+3 =7, 4+5 =9

This leads to the answer.

**In a nutshell: when you encounter problems which ask you to compute the value for n terms**

**Take a small sample and analyze.(Relate the analysis to the answer)**

**Take another sample and analyze**

**Write the result together and derive a relationship among the numbers**

**This leads to the answer.**

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