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Quiz

Year 4: Sequences and progressions

10 questions with solutions for year 4: arithmetic and geometric progressions, sums of the first n terms, infinite geometric series, applications – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. Insert five numbers between 2 and 26 so that all form an arithmetic progression. What is the difference d?

2. Geometric progression: a₁ = 1, q = 2. Which term is 512?

3. A geometric progression with a₅ − a₃ = 36 and a₂ − a₄ = −18:

4. Taxi A: 100 denars start + 50 denars/km; taxi B: 0 start + 60 denars/km. Which is cheaper for 7 km?

5. 50000 denars are shared by 10 people, each getting 1000 less than the one before. How much did the first get?

6. A culture has 30 bacteria and the number doubles every hour. How many are there after the fourth hour?

7. A ball falls from 24 m and after each bounce reaches 3/4 of the previous height. How many metres does it travel before it stops?

8. Igor works 14 days. Plan A: 100, 200, 300, … denars; plan B: 1, 2, 4, 8, … denars. How much does the better plan pay?

9. The sides of a triangle form a geometric progression, the perimeter is 19 and the sum of the squares of the sides is 133. The sides are:

10. The recurring decimal 0.124124… as a fraction is: