Geometric Progression Worksheet

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,ar2,ar3,ar4, ......

Geometric Progression Formula:
The nth term of the G.P is given by,
Tn = a x rn - 1
Sum of n terms is,
Sn = a x (rn - 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 rn - 1
512 = 2 x 2n-1
2n - 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 (rn - 1) / (r - 1)
= 3 x (312 - 1) / (3 - 1)
= 3 x 531440 / 2
= 1594320 / 2
= 797160
Hence the required Sum is 797160.


Similar Worksheets  Arithmetic Progression Worksheet
 Geometric Mean Worksheet
 Math Worksheet to calculate Polynomial Addition
 Worksheet for how to calculate Hypergeometric Distribution
 Worksheet for Standard Deviation Calculation
 Decimal to Hex Conversion Worksheet
 Worksheet for Complex Number Division
 Worksheet to Calculate Sphere Volume & Surface Area
 Worksheet for Vector Dot / Scalar product Calculation
 Worksheet to find Weighted Mean