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,
T_n = a x r^{n - 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 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 (rⁿ - 1) / (r - 1)
= 3 x (312 - 1) / (3 - 1)
= 3 x 531440 / 2
= 1594320 / 2
= 797160
Hence the required Sum is 797160.