A geometric progression is a sequence where each term after the first is obtained by multiplying the preceding term by a constant ratio. The sequence is defined by a starting value and a common ratio used to calculate subsequent terms. For example, in the sequence 1, 3, 9, 27, 81, each term after the first is found by multiplying the prior term by 3, making 3 the common ratio. The general formula for a geometric sequence is a, ar, ar^2, ar^3, where a is the first term and r is the common ratio used to exponentiate subsequent terms.

1. Geometric Progression
•A geometric progression or GP is a sequence
where each new term after the first is obtained by
multiplying the preceding term by a constant r
called common ratio.
•The common ratio is obtained by dividing any
term by the preceding term i.e,

2. • The common ratio is defined only if no term of
the geometric sequence is zero.
• For example, the sequence 1,3,9,27,81 is a
geometric sequence.Note that after first term,
the next term is obtained by multiplying the
preceding term by 3.
• The geometric sequence has its sequence
formation:
a, ar, ar2, ar3, ...

3. General Formula:
Example: Find the 8th term in the Geometric
Progression 1,3,9…..
Sol:

4. Geometric Means
• A number G is said to be a geometric mean
between two numbers a and b if a,G,b are in
G.P. Therefore.
• Geometric Mean = ((X1)(X2)(X3)........(XN))1/N