This worksheet may help you to know about the Geometric Progression. In Geometric Progression each term bears a constant ratio with its preceding term. This constant ratio is called as ratio of the geometrical progression. In Geometrical Progression let a is the first term & r is the common ratio. The general expression of the Geometrical Progression is

a,ar,ar^{2},ar^{3},ar^{4}, ......

**Geometric Progression Formula:**

The nth term of the G.P is given by,

T_{n} = a x r^{n - 1}

Sum of n terms is,

Sn = a x (r^{n} - 1) / (r - 1)

**Geometric Progression Examples:****Example 1**

How many terms are there in 2,4,8,16, ....,512.

__Solution:__

Here a = 2 & r = 4/2 = 2.

Tn = a x r^{n - 1}

512 = 2 x 2^{n-1}

2^{n - 1} = 256 = 28

n - 1 = 8

n = 9

**Example 2**

Find the value of 3 + 32 + 33 + 34 + .... + 312 = ?
__Solution:__

Here a = 3 & r = 3 , n = 12

Sn = a x (r^{n} - 1) / (r - 1)

= 3 x (312 - 1) / (3 - 1)

= 3 x 531440 / 2

= 1594320 / 2

= 797160

Hence the required Sum is 797160.

Math Calculators

- Standard Deviation Calculator
- Probability Calculator
- Frequency Converter
- Square Calculator
- Circle Calculator
- Cylinder Calculator
- Midpoint Calculator
- Slope Intercept Form Calculator
- Radical Equation Calculator
- Quadratic Equation Calculator
- Percentage Calculator
- Log Calculator
- Fraction to Decimal calculator
- Radical Calculator
- LCM Calculator