The triangular numbers begin 1, 3, 6, 10, 15, ... What is the sum of the 9th and 10th triangular numbers?
Answer and explanation
Correct answer: D. 100
- Step 1: The nth triangular number is 1 + 2 + ... + n, so the 9th is 45 and the 10th is 55. Step 2. 45 + 55 = 100. Answer: 100. Why not the others: 55: This is the 10th triangular number only. 45: This is the 9th triangular number only. 121: This is the sum of the 10th and 11th triangular numbers.
Practise more Algebra, ratio and problem solving.
Free questions with an explanation for every one, and full timed Independent School Entrance (ISEB Pre-Test and 11+ CEM style) mock tests.
More Algebra, ratio and problem solving questions
- Solve 4(2x - 3) = 3x + 13.
- Three consecutive odd numbers add up to 99. What is the largest of them?
- If a = 3 and b = -2, what is the value of a² - 2ab + b²?
- The first terms of a sequence are 7, 11, 15, 19. What is the 50th term?
- The ratio of boys to girls in a club is 3 : 5. When 6 more boys join, the numbers of boys and girls are equal. How many members were in the…
- Pasta is sold in three packs: 750 g for £1.80, 500 g for £1.15 and 1.2 kg for £2.64. Which pack is the cheapest per 100 g?