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We have seen iterative processes in real life. It also can be seen in number sequences.
A number sequence is obtained by doing repetitive operation. It may increase or decrease during the process.
Let's see some examples of number sequences.
Example:
1. Add \(4\) with the starting number \(3\), you will get the number \(7\). Now add \(4\) with the resultant \(7\), you will get the number \(11\), again add \(4\) with the new resulting \(11\), this process goes on.
Here, adding \(4\) is the iterative process.
\(3 + 4\), \(7 + 4\), \(11 + 4\), \(15 + 4\), …
The sequence obtained is \(3\), \(7\), \(11\), \(16\), …
2. Subtract \(3\) from the starting number \(99\), you will get the number \(96\). Now subtract \(3\) from the resultant \(96\), you will get the number \(93\), again subtract \(3\) from the new resulting \(93\), this process goes on.
Here, subtracting \(3\) is the iterative process.
\(99 - 3\), \(96 - 3\), \(93 - 3\), \(90 - 3\), …
The sequence obtained is \(99\), \(96\), \(93\), \(90\), …
3. Multiply the starting number \(1\) by \(4\), you will get the number \(4\). Now multiply the resultant \(4\) by \(4\), you will get the number \(16\). Multiply the new resulting \(16\) by \(4\); this process goes on.
Here, multiplying \(4\) is the iterative process.
\(1 \times 4\), \(4 \times 4\), \(16 \times 4\), \(64 \times 4\)…
The sequence obtained is \(4\), \(16\), \(64\), \(256\), …
4. \(5\), \(50\), \(500\), …
In this pattern, the values get increased when the number of zeroes increased.
5. \(3\), \(9\), \(27\), \(81\), …
This pattern is obtained by generating \(3 \times 3^0\), \(3 \times 3^1\), \(3 \times 3^2\), \(3 \times 3^3\)…
6. \(1\), \(11\), \(111\), \(1111\), …
In this pattern, the values get increased when the number of ones increased.
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