Arithmetic Geometric And Harmonic Progressions Formulas

Formulas of Geometric Progression (G.P)

Suppose, if ‘a’ is the first term and ‘r’ be the common ration, then

• Formula for nth term of GP = a r ^n-1
• Geometric mean = nth root of the product of ‘n’ terms in the GP.
• Formula to find the geometric mean between two quantities a and b = \sqrt{ab}
• Formula to find the sum of the number of terms in a GP

Let ‘a’ be the first term, ‘r’ be the common ratio and ‘n’ be the number of terms

1. 1. if r>1 , then , s_{n} = a \times \frac{r^{n} -1}{r-1}
   2. if r<1 , then , s_{n} = a \times \frac{1-r^{n}}{1-r}

Sum of infinite terms in a GP(r<1) \frac{a}{1-r}