Now, if you have understood the method of adding a sequence of numbers try to solve the following example:
Imagine a mammoth pile of logs stacked in the manner shown at the left. Suppose there are 113 logs in the bottom row. How many logs are there in the whole pile?
To understand the way we add the sequence, see some interesting diagrams These diagrams help us understand what actually happens when we add a sequence by writing the same sequence below the original one in the reverse order. A rectangle of objects (representing the addition of two numbers in a pair) gets formed. Since we actually need to count the objects lying in half of the rectangle, we divide the total number of objects obtained by half. You can see the alignment of objects in a square by selecting any number you want.
There is yet another interesting day to day example where we will be finding this quicker method of adding sequential numbers useful. Suppose we have a clock which struck from 1 to 24. How many strokes in all will be there in twenty-four hours?
Using the shorter method we know that the answer is (1 + 24) × 24 ÷ 2 = 300.
The type of sequence we have talked about so far is called an arithmetic sequence. This type of sequence always increases or decreases by adding or subtracting the same number.
Even if the sequence starts from any other number than 1, the same trick may be used to add the given sequence.
Suppose our sequence is 4 + 5 + 6 + . . . . .+ 18 + 19 + 20. When you have such a sequence the difficulty lies only in determining the number of pairs you will be adding. Otherwise all other logic will remain the same. Here, the number of pairs will be (20 - 4) + 1, i.e. 17. Then the sum of the sequence would be (4 + 20) × 17 ÷ 2 = 12 × 17 = 204.
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