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Formulas

Arithmetic and geometric sequences have formulas so that you can find any term in the sequence.

Here are the formulae regarding arithmetic sequences: un = a + [(n - 1) × d] Sn = n[2a + (n - 1) × d]/2
 * Finding the nth term:
 * Finding the sum of the first n terms:

 a = the first term in the sequence

n = the term number (1st term, 2nd term, 3rd term, etc.)

d = the common difference (difference between consecutive terms) 

''' What are these formulae and why do they work? '''

Let's start with the first formula. un = a + [(n - 1) × d]

We'll try it out with an example, say this sequence:

The first part of the formula has "a," which makes sense, it being the first term.

The second part gets a little trickier. [(n - 1) × d]

For the first term, the formula results in "a," which is expected.

For the second term, the formula results in "a + d." This signifies that the second term has the common difference added to it.

For the third term, the formula results in "a + 2d." Another common difference was added to the previous term.

This is why the formula works; it