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