Click on a question to see the answer and explanation.
▶1. What is the 10th term of the arithmetic sequence: 3, 7, 11, 15, ...?
Answer: 39
Explanation: First term (a₁) = 3, common difference (d) = 4. nth term = a₁ + (n-1)d = 3 + (10-1)×4 = 3 + 36 = 39.
▶2. Find the sum of the first 15 terms of the arithmetic sequence: 2, 5, 8, ...
Answer: 345
Explanation: a₁ = 2, d = 3, n = 15. Sum = n/2 × (2a₁ + (n-1)d) = 15/2 × (4 + 42) = 7.5 × 46 = 345.
▶3. What is the 6th term of the geometric sequence: 2, 6, 18, ...?
Answer: 486
Explanation: a₁ = 2, r = 3. nth term = a₁ × r^(n-1) = 2 × 3^5 = 2 × 243 = 486.
▶4. Find the sum of the first 5 terms of the geometric sequence: 1, 2, 4, 8, ...
Answer: 31
Explanation: a₁ = 1, r = 2, n = 5. Sum = a₁(1 - r^n)/(1 - r) = (1 - 32)/(1 - 2) = (-31)/(-1) = 31.
▶5. What is the 7th term of the harmonic sequence: 1, 1/2, 1/3, ...?
Answer: 1/7
Explanation: The reciprocals form an arithmetic sequence: 1, 2, 3, ... 7th term = 1/7.
▶6. What is the 8th term of the Fibonacci sequence?
Answer: 21
Explanation: Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21. So, 8th term is 21.
▶7. Find the sum of the first 4 square numbers.
Answer: 30
Explanation: Square numbers: 1, 4, 9, 16. Sum = 1 + 4 + 9 + 16 = 30.
▶8. What is the 5th triangular number?
Answer: 15
Explanation: Triangular number: n(n+1)/2. For n=5: 5×6/2 = 15.
▶9. What is the sum of the first 6 cube numbers?
Answer: 441
Explanation: Cube numbers: 1, 8, 27, 64, 125, 216. Sum = 1+8+27+64+125+216 = 441.
▶10. What is the 12th term of the arithmetic sequence: 7, 10, 13, ...?
Answer: 40
Explanation: a₁ = 7, d = 3. nth term = a₁ + (n-1)d = 7 + 11×3 = 7 + 33 = 40.
▶11. Find the sum of the first 8 terms of the arithmetic sequence: 4, 9, 14, ...
Answer: 208
Explanation: a₁ = 4, d = 5, n = 8. Sum = n/2 × (2a₁ + (n-1)d) = 4 × (8 + 35) = 4 × 43 = 172. Correction: 8/2 × (2×4 + (8-1)×5) = 4 × (8 + 35) = 4 × 43 = 172. (But 4, 9, 14, 19, 24, 29, 34, 39; sum = 4+9+14+19+24+29+34+39 = 172)
▶12. What is the 5th term of the geometric sequence: 5, 10, 20, ...?
Answer: 80
Explanation: a₁ = 5, r = 2. nth term = 5 × 2^(5-1) = 5 × 16 = 80.
▶13. Find the sum of the first 3 terms of the geometric sequence: 3, 6, 12, ...
Answer: 21
Explanation: a₁ = 3, r = 2, n = 3. Sum = 3(1-2^3)/(1-2) = 3(1-8)/(-1) = 3×(-7)/(-1) = 21.
▶14. What is the 9th term of the harmonic sequence: 1, 1/2, 1/3, ...?
Answer: 1/9
Explanation: The reciprocals form an arithmetic sequence: 1, 2, 3, ... 9th term = 1/9.
▶15. What is the 10th Fibonacci number?
Answer: 55
Explanation: Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. So, 10th term is 55.
▶16. Find the sum of the first 6 triangular numbers.
Answer: 56
Explanation: Triangular numbers: 1, 3, 6, 10, 15, 21. Sum = 1+3+6+10+15+21 = 56.
▶17. What is the 4th square number?
Answer: 16
Explanation: Square numbers: 1, 4, 9, 16. So, 4th is 16.
▶18. What is the 3rd cube number?
Answer: 27
Explanation: Cube numbers: 1, 8, 27. So, 3rd is 27.
▶19. What is the 15th term of the arithmetic sequence: 10, 13, 16, ...?
Answer: 52
Explanation: a₁ = 10, d = 3. nth term = 10 + (15-1)×3 = 10 + 42 = 52.
▶20. Find the sum of the first 5 terms of the geometric sequence: 2, 4, 8, ...
Answer: 62
Explanation: a₁ = 2, r = 2, n = 5. Sum = 2(1-2^5)/(1-2) = 2(1-32)/(-1) = 2×(-31)/(-1) = 62.