MathsAges 16-18

Geometric series sum

Sum the first n terms of a geometric progression using Sₙ = a(rⁿ − 1) ÷ (r − 1). Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Geometric series sum

Take your time. Show your thinking.

1. Find the sum of the first 4 terms of the geometric series with first term a = 2 and common ratio r = 2.
4 · 2 · 2 · Geometric series sum
2. Find the sum of the first 3 terms of the geometric series with first term a = 3 and common ratio r = 3.
3 · 3 · 3 · Geometric series sum
3. Find the sum of the first 3 terms of the geometric series with first term a = 4 and common ratio r = 3.
3 · 4 · 3 · Geometric series sum
4. Find the sum of the first 5 terms of the geometric series with first term a = 2 and common ratio r = 3.
5 · 2 · 3 · Geometric series sum
5. Find the sum of the first 4 terms of the geometric series with first term a = 3 and common ratio r = 2.
4 · 3 · 2 · Geometric series sum
6. Find the sum of the first 3 terms of the geometric series with first term a = 6 and common ratio r = 3.
3 · 6 · 3 · Geometric series sum
7. Find the sum of the first 4 terms of the geometric series with first term a = 1 and common ratio r = 3.
4 · 1 · 3 · Geometric series sum
8. Find the sum of the first 4 terms of the geometric series with first term a = 4 and common ratio r = 3.
4 · 4 · 3 · Geometric series sum
9. Find the sum of the first 5 terms of the geometric series with first term a = 8 and common ratio r = 3.
5 · 8 · 3 · Geometric series sum
10. Find the sum of the first 5 terms of the geometric series with first term a = 3 and common ratio r = 2.
5 · 3 · 2 · Geometric series sum
11. Find the sum of the first 3 terms of the geometric series with first term a = 8 and common ratio r = 2.
3 · 8 · 2 · Geometric series sum
12. Find the sum of the first 4 terms of the geometric series with first term a = 6 and common ratio r = 3.
4 · 6 · 3 · Geometric series sum

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Geometric series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 4 terms of the geometric series with first term a = 2 and common ratio r = 2.
30
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 2(2^4 − 1) ÷ (2 − 1) = 30.
2. Find the sum of the first 3 terms of the geometric series with first term a = 3 and common ratio r = 3.
39
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(3^3 − 1) ÷ (3 − 1) = 39.
3. Find the sum of the first 3 terms of the geometric series with first term a = 4 and common ratio r = 3.
52
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 4(3^3 − 1) ÷ (3 − 1) = 52.
4. Find the sum of the first 5 terms of the geometric series with first term a = 2 and common ratio r = 3.
242
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 2(3^5 − 1) ÷ (3 − 1) = 242.
5. Find the sum of the first 4 terms of the geometric series with first term a = 3 and common ratio r = 2.
45
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(2^4 − 1) ÷ (2 − 1) = 45.
6. Find the sum of the first 3 terms of the geometric series with first term a = 6 and common ratio r = 3.
78
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 6(3^3 − 1) ÷ (3 − 1) = 78.
7. Find the sum of the first 4 terms of the geometric series with first term a = 1 and common ratio r = 3.
40
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 1(3^4 − 1) ÷ (3 − 1) = 40.
8. Find the sum of the first 4 terms of the geometric series with first term a = 4 and common ratio r = 3.
160
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 4(3^4 − 1) ÷ (3 − 1) = 160.
9. Find the sum of the first 5 terms of the geometric series with first term a = 8 and common ratio r = 3.
968
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 8(3^5 − 1) ÷ (3 − 1) = 968.
10. Find the sum of the first 5 terms of the geometric series with first term a = 3 and common ratio r = 2.
93
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(2^5 − 1) ÷ (2 − 1) = 93.
11. Find the sum of the first 3 terms of the geometric series with first term a = 8 and common ratio r = 2.
56
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 8(2^3 − 1) ÷ (2 − 1) = 56.
12. Find the sum of the first 4 terms of the geometric series with first term a = 6 and common ratio r = 3.
240
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 6(3^4 − 1) ÷ (3 − 1) = 240.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Geometric series sum

Take your time. Show your thinking.

1. Find the sum of the first 4 terms of the geometric series with first term a = 2 and common ratio r = 2.
4 · 2 · 2 · Geometric series sum
2. Find the sum of the first 3 terms of the geometric series with first term a = 3 and common ratio r = 3.
3 · 3 · 3 · Geometric series sum
3. Find the sum of the first 3 terms of the geometric series with first term a = 4 and common ratio r = 3.
3 · 4 · 3 · Geometric series sum
4. Find the sum of the first 5 terms of the geometric series with first term a = 2 and common ratio r = 3.
5 · 2 · 3 · Geometric series sum
5. Find the sum of the first 4 terms of the geometric series with first term a = 3 and common ratio r = 2.
4 · 3 · 2 · Geometric series sum
6. Find the sum of the first 3 terms of the geometric series with first term a = 6 and common ratio r = 3.
3 · 6 · 3 · Geometric series sum
7. Find the sum of the first 4 terms of the geometric series with first term a = 1 and common ratio r = 3.
4 · 1 · 3 · Geometric series sum
8. Find the sum of the first 4 terms of the geometric series with first term a = 4 and common ratio r = 3.
4 · 4 · 3 · Geometric series sum
9. Find the sum of the first 5 terms of the geometric series with first term a = 8 and common ratio r = 3.
5 · 8 · 3 · Geometric series sum
10. Find the sum of the first 5 terms of the geometric series with first term a = 3 and common ratio r = 2.
5 · 3 · 2 · Geometric series sum
11. Find the sum of the first 3 terms of the geometric series with first term a = 8 and common ratio r = 2.
3 · 8 · 2 · Geometric series sum
12. Find the sum of the first 4 terms of the geometric series with first term a = 6 and common ratio r = 3.
4 · 6 · 3 · Geometric series sum

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Geometric series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 4 terms of the geometric series with first term a = 2 and common ratio r = 2.
30
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 2(2^4 − 1) ÷ (2 − 1) = 30.
2. Find the sum of the first 3 terms of the geometric series with first term a = 3 and common ratio r = 3.
39
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(3^3 − 1) ÷ (3 − 1) = 39.
3. Find the sum of the first 3 terms of the geometric series with first term a = 4 and common ratio r = 3.
52
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 4(3^3 − 1) ÷ (3 − 1) = 52.
4. Find the sum of the first 5 terms of the geometric series with first term a = 2 and common ratio r = 3.
242
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 2(3^5 − 1) ÷ (3 − 1) = 242.
5. Find the sum of the first 4 terms of the geometric series with first term a = 3 and common ratio r = 2.
45
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(2^4 − 1) ÷ (2 − 1) = 45.
6. Find the sum of the first 3 terms of the geometric series with first term a = 6 and common ratio r = 3.
78
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 6(3^3 − 1) ÷ (3 − 1) = 78.
7. Find the sum of the first 4 terms of the geometric series with first term a = 1 and common ratio r = 3.
40
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 1(3^4 − 1) ÷ (3 − 1) = 40.
8. Find the sum of the first 4 terms of the geometric series with first term a = 4 and common ratio r = 3.
160
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 4(3^4 − 1) ÷ (3 − 1) = 160.
9. Find the sum of the first 5 terms of the geometric series with first term a = 8 and common ratio r = 3.
968
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 8(3^5 − 1) ÷ (3 − 1) = 968.
10. Find the sum of the first 5 terms of the geometric series with first term a = 3 and common ratio r = 2.
93
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(2^5 − 1) ÷ (2 − 1) = 93.
11. Find the sum of the first 3 terms of the geometric series with first term a = 8 and common ratio r = 2.
56
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 8(2^3 − 1) ÷ (2 − 1) = 56.
12. Find the sum of the first 4 terms of the geometric series with first term a = 6 and common ratio r = 3.
240
Sₙ = a(rⁿ − 1) ÷ (r − 1) = 6(3^4 − 1) ÷ (3 − 1) = 240.

12 questions · Seed 44 · Age guidance, not curriculum certification