→The sequence whose common ratio between the two successive terms are same is called geometric sequence.
For example:3, 9, 27, 81……..
General term of Geometric Progression is given by;
tn= nth term of sequence
a = first term of sequence
n = nth term of sequence
r = common ratio of sequence
Geometric Mean: The term/s in between the first and last term in the arithmetic progression is/are called geometric means.
Example; i) 2, 4, 8 ii) 4, -8, 16, -32, 64
Here, the highlighted terms are the geometric means.
Formulas related to Geometric Means:
→The single geometric mean between two terms a & b is calculated by;
→If there are n terms between ‘a’ and ‘b’ then the common ratio is given by;
Here, n does represent number of terms in the sequence but number of means between first and last term.
Sum of GP
→ [when 1st term and number of terms are given & r >1]
→ [when 1st term and number of terms are given & r <1]
→ [when 1st and last terms are given & r >1]
→ [when 1st and last terms are given & r <1]