How to Solve Finite Geometric Series? (+FREE Worksheet!)
Want to learn more about Finite Geometric Series? Take a look at the following step-by-step guide to solve Finite Geometric Series problems.
Related Topics
- How to Solve Infinite Geometric Series
- How to Solve Geometric Sequences
- How to Solve Arithmetic Sequences
Step by step guide to solve Finite Geometric Series
- The sum of a geometric series is finite when the absolute value of the ratio is less than 1.
- Finite Geometric Series formula: Sn=∑ni=1ari−1=a1(1−rn1−r)
Finite Geometric Series – Example 1:
Evaluate the geometric series described. Sn=∑5n=13n−1
Solution:
Use this formula: Sn=∑ni=1ari−1=a1(1−rn1−r)→Sn=∑5n=13n−1=(1)(1−351−3)→(1)(1−351−3)=121
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Finite Geometric Series – Example 2:
Evaluate the geometric series described. Sn=∑3n=1−4n−1
Solution:
Use this formula: Sn=∑ni=1ari−1=a1(1−rn1−r)→Sn=∑3n=1−4n−1=(−1)(1−431−4)→(−1)(1−451−4)=−21
Finite Geometric Series – Example 3:
Evaluate the geometric series described. Sn=∑7n=12n−1
Solution:
Use this formula: Sn=∑ni=1ari−1=a1(1−rn1−r)→Sn=∑7n=12n−1=1(1−271−2)→(1−1281−2)=(−127−1)=127
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Finite Geometric Series – Example 4:
Evaluate the geometric series described. Sn=∑4n=1−5n−1
Solution:
Use this formula: Sn=∑ni=1ari−1=a1(1−rn1−r)→Sn=∑4n=1−5n−1=(−1)(1−541−5)=(−1)(1−6251−5)=(−1)(–624−4)=(−1)(6244)=−156
Exercises for Solving Finite Geometric Series
Evaluate each geometric series described.
- 1–5+25–125…,n=7
- –3–6–12–24…,n=9
- ∑8n=12,(−2)n−1
- ∑9n=14,3n−1
- ∑10n=14,(−3)n−1
- ∑9m=1−2m−1
- 13021
- –1533
- –170
- 39364
- –59048
- –511
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