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  Geometric Mean Worksheet
 Arithmetic Progression Worksheet
 Math Worksheet to find n Factorial value
 Worksheet for how to calculate Class Interval Arithmetic Mean
 Worksheet for Skewness Calculation
 Worksheet for Decimal to Binary Conversion
 Worksheet for Complex Number Multiplication
 Worksheet to Calculate Triangle Area
 Worksheet for Vector Cross product Calculation
 Worksheet for Vector Subtraction