Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple for- mula or rule.

A sequence can be arithmetic, geometric or neither

The first three terms are given as:

3, 5, 7

The above terms have a common difference of 2.

So, the first sequence is f(n) = 1 + 2n

Another rule is to subtract a term from the product of 4 and the previous term.

So, we have: f(n+2) = 4f(n) - f(n + 1)

Also, we can subtract a 8 from the product of consecutive terms.

So, we have: f(n+2) = f(n) * f(n + 1) - 8

Read more about sequence and series at:

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1. Perhaps the simplest rule is one that makes this the start of an arithmetic sequence:

Then the sequence will continue ...

... 3, 5, 7, 9, 11, 13, 15, ...

2. We can multiply the two terms by some values, add the results, then add some constant. There are an infinite number of ways to choose such values. Here's one set of numbers that give the third term from the first two:

Then the sequence will continue ...

... 3, 5, 7, 13, 15, 37, 23, ...

3. We can multiply adjacent values and add a constant.

Then the sequence will continue ...

... 3, 5, 7, 28, 188, 5256, 988120, ...

2x^2+5x+17

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