Geometric Progression(G.P.) is a sequence of numbers which is generated by multiplying a common ratio (r) from the previous number.

**Nth term of Geometric progression**

a_{n} = a_{1} r^{n-1}

Where:

Where:

a_{n} = The nth term

a_{1} = The 1st term

r = The common ratio \(\frac{{{a_2}}}{{{a_1}}}\)

n = number of terms

**Summation of a Geometric Progression**

\(S = \frac{{{a_1}\left( {1 - {r^n}} \right)}}{{1 - r}}\)

But if \( |r| < 1\) and n approaches a large number (infinity): r^{n} = 0

Thus:

\(S = \frac{{{a_1}}}{{1 - r}}\)

a

Where:

Where:

a

a

r = The common ratio \(\frac{{{a_2}}}{{{a_1}}}\)

n = number of terms

\(S = \frac{{{a_1}\left( {1 - {r^n}} \right)}}{{1 - r}}\)

But if \( |r| < 1\) and n approaches a large number (infinity): r

Thus:

\(S = \frac{{{a_1}}}{{1 - r}}\)