Sum of a Finite Geometric Series
Aligned to A-SSE.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
A geometric series adds terms with a constant ratio r. The sum of n terms starting at a is S = a(1 − r^n)/(1 − r), which comes from subtracting r×S from S to cancel the middle terms.
Worked example
Find 3 + 6 + 12 + 24 + 48. Here a = 3, r = 2, and n = 5 terms. S = 3(1 − 2^5)/(1 − 2) = 3(1 − 32)/(−1) = 3(−31)/(−1) = 93.
Practice questions
- Find the sum 5 + 15 + 45 + 135.
- Use the formula to sum the first 6 terms of a = 2, r = 3.
- A ball drops and each bounce is 1/2 the height: sum 100 + 50 + 25 + 12.5.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Suma de una Serie Geométrica Finita
Una serie geométrica suma términos con una razón constante r. La suma de n términos que empieza en a es S = a(1 − r^n)/(1 − r), que se obtiene al restar r×S de S para cancelar los términos intermedios.
Ejemplo: Encuentra 3 + 6 + 12 + 24 + 48. Aquí a = 3, r = 2, y n = 5 términos. S = 3(1 − 2^5)/(1 − 2) = 3(1 − 32)/(−1) = 3(−31)/(−1) = 93.
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