Geometric Progression
- If in a succession of numbers the ratio of any term and the previous term is constant then that numbers are said to be in Geometric Progression.
- Ex :1, 3, 9, 27 or a, ar, a$$r^{2}$$, a$$r^{3}$$
- The general expression of a G.P, Tn = a $$r^{n-1}$$ (where a is the first term and ‘r’ is the common ratio).
- Sum of ‘n’ terms in G.P, Sn = $$\frac{a(1-r^{n})}{1-r}$$ (if r<1) or $$\frac {a(r^{n}-1)}{r-1}$$ (if r>1)
Properties of G.P
If a, b , c, d,.... are in G.P and ‘k’ is a constant then
- ak, bk, ck,...will also be in G.P
- a/k, b/k, c/k will also be in G.P
Sum of term of infinite series in G.P, $$S_{∞}$$=$$\frac {a}{1-r}$$ (-1 < r <1)
