How to Solve Finite Geometric Series? (+FREE Worksheet!)
A finite geometric series adds a fixed number of terms where each is the previous one multiplied by a constant ratio. Its sum is the first term times one minus the ratio to the power of n, all divided by one minus the ratio.
Tutor-style math help
Solve Finite Geometric Series: what to notice and how to work it
Series skill
Sequences list terms; series add terms. The first question is whether the pattern adds the same amount or multiplies by the same factor.
What to notice first
Identify the term number. Many mistakes happen because (a_1), (a_n), and the number of terms get mixed up.
Common student mistake
Do not use an arithmetic formula on a geometric pattern. Check differences and ratios before choosing a formula.
Key formulas and cues
(a_n=a_1+(n-1)d)
(a_n=a_1r^{n-1})
(S_n=frac{n}{2}(a_1+a_n))
(S_n=a_1frac{1-r^n}{1-r})
A reliable path
- Compare termsLook for a common difference or common ratio.
- Choose term or sumDecide whether the question asks for one term or a total.
- Track nMake sure n is the position or number of terms the question uses.
Worked examples
Arithmetic sequence
Example: 5, 9, 13, 17, …
- Each term adds 4.
- The common difference is 4.
- Add 4 to continue.
Answer: (21)
Geometric sequence
Example: 3, 6, 12, 24, …
- Each term multiplies by 2.
- The common ratio is 2.
- Multiply 24 by 2.
Answer: (48)
Try one before moving on
Try: Find the next term: 10, 7, 4, 1, …
Answer: (-2). The pattern subtracts 3.
Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.
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Solve Finite Geometric Series: pop-up practice
Answer these quick questions, then use the feedback to decide which part of the lesson to review.
Choose an answer to begin.
1. 2, 5, 8, 11, … is:
2. 4, 12, 36, … has common ratio:
3. A series asks you to:
Exercises for Solving Finite Geometric Series
Evaluate each geometric series described.
- (color{blue}{1 – 5 + 25 – 125 …, n = 7})
- (color{blue}{-3 -6 -12 – 24 …, n = 9})
- (color{blue}{ sum_{n=1}^8 2, (-2)^{n-1}} \ )
- (color{blue}{ sum_{n=1}^9 4, 3^{n-1} } \ )
- (color{blue}{ sum_{n=1}^{10} 4, (-3)^{n-1} } \ )
- (color{blue}{ sum_{m=1}^9 -2^{m-1} } \ )
- (color{blue}{13021})
- (color{blue}{-1533})
- (color{blue}{-170})
- (color{blue}{39364})
- (color{blue}{-59048})
- (color{blue}{-511})
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