The Geometric Sequence Finite Sum
To compute the sum of a finite geometric sequence, we can use the formula:
Sn = a(1 – r^n) / (1 – r)
Where:
– Sn is the sum of the first n terms in the geometric sequence
To compute the sum of a finite geometric sequence, we can use the formula:
Sn = a(1 – r^n) / (1 – r)
Where:
– Sn is the sum of the first n terms in the geometric sequence.
– a is the first term of the sequence.
– r is the common ratio between consecutive terms in the sequence.
– n is the number of terms in the sequence.
Let’s work through an example to illustrate how to use this formula:
Example:
Find the sum of the geometric sequence: 2, 4, 8, 16, 32 with 5 terms.
Solution:
In this sequence, the first term (a) is 2, the common ratio (r) is 4/2 = 2, and the number of terms (n) is 5.
Plugging these values into the formula:
Sn = a(1 – r^n) / (1 – r)
= 2(1 – 2^5) / (1 – 2)
= 2(1 – 32) / (1 – 2)
= 2(-31) / (-1)
= 62
Therefore, the sum of the geometric sequence 2, 4, 8, 16, 32 with 5 terms is 62.
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