MathsAges 16-18

Arithmetic series sum

Sum the first n terms of an arithmetic progression using Sₙ = (n ÷ 2)(2a + (n − 1)d). Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Arithmetic series sum

Take your time. Show your thinking.

1. Find the sum of the first 12 terms of the arithmetic series with first term a = 7 and common difference d = 9.
12 · 7 · 9 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 6.
4 · 15 · 6 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 2.
12 · 12 · 2 · Arithmetic series sum
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 4.
6 · 5 · 4 · Arithmetic series sum
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 6.
14 · 12 · 6 · Arithmetic series sum
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 3.
14 · 14 · 3 · Arithmetic series sum
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 3.
6 · 1 · 3 · Arithmetic series sum
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 9 and common difference d = 8.
12 · 9 · 8 · Arithmetic series sum
9. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 4.
12 · 2 · 4 · Arithmetic series sum
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 2.
14 · 10 · 2 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 5.
10 · 13 · 5 · Arithmetic series sum
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
4 · 9 · 4 · Arithmetic series sum

12 questions · Seed 48 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Arithmetic series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 12 terms of the arithmetic series with first term a = 7 and common difference d = 9.
678
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 7 + 11 × 9) = 678.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 6.
96
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 6) = 96.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 2.
276
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 12 + 11 × 2) = 276.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 4.
90
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 4) = 90.
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 6.
714
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 12 + 13 × 6) = 714.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 3.
469
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 14 + 13 × 3) = 469.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 3.
51
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 3) = 51.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 9 and common difference d = 8.
636
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 9 + 11 × 8) = 636.
9. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 4.
288
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 4) = 288.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 2.
322
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 10 + 13 × 2) = 322.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 5.
355
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 5) = 355.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 4) = 60.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Arithmetic series sum

Take your time. Show your thinking.

1. Find the sum of the first 12 terms of the arithmetic series with first term a = 7 and common difference d = 9.
12 · 7 · 9 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 6.
4 · 15 · 6 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 2.
12 · 12 · 2 · Arithmetic series sum
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 4.
6 · 5 · 4 · Arithmetic series sum
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 6.
14 · 12 · 6 · Arithmetic series sum
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 3.
14 · 14 · 3 · Arithmetic series sum
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 3.
6 · 1 · 3 · Arithmetic series sum
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 9 and common difference d = 8.
12 · 9 · 8 · Arithmetic series sum
9. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 4.
12 · 2 · 4 · Arithmetic series sum
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 2.
14 · 10 · 2 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 5.
10 · 13 · 5 · Arithmetic series sum
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
4 · 9 · 4 · Arithmetic series sum

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Arithmetic series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 12 terms of the arithmetic series with first term a = 7 and common difference d = 9.
678
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 7 + 11 × 9) = 678.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 6.
96
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 6) = 96.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 2.
276
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 12 + 11 × 2) = 276.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 4.
90
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 4) = 90.
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 6.
714
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 12 + 13 × 6) = 714.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 3.
469
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 14 + 13 × 3) = 469.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 3.
51
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 3) = 51.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 9 and common difference d = 8.
636
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 9 + 11 × 8) = 636.
9. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 4.
288
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 4) = 288.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 2.
322
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 10 + 13 × 2) = 322.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 5.
355
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 5) = 355.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 4) = 60.

12 questions · Seed 48 · Age guidance, not curriculum certification