Sum of geometric series formula

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Geometric sequence is the order of numbers where we get the next term in the sequence by multiplying its previous term by a constant. If the numbers in the geometric sequence are added together, then that forms a geometric series. In the geometric series, the common ratio is calculated by dividing any two numbers next to each other in the series. Sum of the numbers in a geometric series is given by the formula = a (1 – rn)/ (1 – r).
 
Example 1: Find the sum of the first 4 terms of the geometric sequence: 4, 8, 16, 32, 64 …

Given the geometric sequence: 4, 8, 16, 32, 64 …
Sum of the numbers in a geometric series formula= a (1– rn)/ (1– r)
Here, ‘a’= first term= 4
‘r’ is the common ratio, which is the constant ratio between any two adjacent numbers in the geometric sequence==> 8/4= 2
‘n’ = number of terms= 4
So, Sum= 4 (1– 24)/ (1– 2) ==>Sum= 4 (1– 16)/ (-1) = 60

Therefore, sum of the given geometric series= 60
 
Example 2: Find the sum of the first 5 terms of the geometric sequence: 3, 9, 27, 81, 243 …
Given the geometric sequence: 3, 9, 27, 81, 243 …
Sum of the numbers in a geometric series formula= a (1– rn)/ (1– r)
Here, ‘a’= first term= 3
‘r’ is the common ratio, which is the constant ratio between any two adjacent numbers in the geometric sequence==> 9/3= 3
‘n’ = number of terms= 5
So, Sum= 3 (1– 35)/ (1– 3) ==>Sum= 3 (1– 243)/ (-2) = 363

Therefore, sum of the given geometric series= 363

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