Sequences: Geometric Progression and Sequence
Questions from Questionbank
Topic 1. Sequences and Series, Exponentials and The Binomial Theorem
1. Find the sum of the arithmetic series
17 + 27 + 37 +...+ 417.
2. Find the coefficient of x5 in the expansion of (3x – 2)8.
3. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series.
4. Find the coefficient of a3b4 in the expansion of (5a + b)7.
5. Solve the equation 43x–1 = 1.5625 × 10–2.
6. In an arithmetic sequence, the first term is 5 and the fourth term is 40. Find the second term.
7. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for
(a) log2 5; (b) loga 20.
8. Find the sum of the infinite geometric series 9. Find the coefficient of a5b7 in the expansion of (a + b)12.
10. The Acme insurance company sells two savings plans, Plan A and Plan B. For Plan A, an investor starts with an initial deposit of $1000 and increases this by $80 each month, so that in the second month, the deposit is $1080, the next month it is $1160 and so on. For Plan B, the investor again starts with $1000 and each month deposits 6% more than the previous month.
(a) Write down the amount of money invested under Plan B in the second and third months.
Give your answers to parts (b) and (c) correct to the nearest dollar.
(b) Find the amount of the 12th deposit for each Plan.
(c) Find the total amount of money invested during the first 12 months
(i) under Plan A;
(ii) under Plan B.
11. $1000 is invested at the beginning of each year for 10 years. The rate of interest is fixed at 7.5% per annum. Interest is compounded annually. Calculate, giving your answers to the nearest dollar
(a) how much the first $1000 is worth at the end of the ten years; (b) the total value of the investments at the end of the ten years.
12. Let log10P = x , log10Q = y and log10R = z. Express in terms of x , y and z.
13. Each day a runner trains for a 10 km race. On the first day
Topic 1. Sequences and Series, Exponentials and The Binomial Theorem
1. Find the sum of the arithmetic series
17 + 27 + 37 +...+ 417.
2. Find the coefficient of x5 in the expansion of (3x – 2)8.
3. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series.
4. Find the coefficient of a3b4 in the expansion of (5a + b)7.
5. Solve the equation 43x–1 = 1.5625 × 10–2.
6. In an arithmetic sequence, the first term is 5 and the fourth term is 40. Find the second term.
7. If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for
(a) log2 5; (b) loga 20.
8. Find the sum of the infinite geometric series 9. Find the coefficient of a5b7 in the expansion of (a + b)12.
10. The Acme insurance company sells two savings plans, Plan A and Plan B. For Plan A, an investor starts with an initial deposit of $1000 and increases this by $80 each month, so that in the second month, the deposit is $1080, the next month it is $1160 and so on. For Plan B, the investor again starts with $1000 and each month deposits 6% more than the previous month.
(a) Write down the amount of money invested under Plan B in the second and third months.
Give your answers to parts (b) and (c) correct to the nearest dollar.
(b) Find the amount of the 12th deposit for each Plan.
(c) Find the total amount of money invested during the first 12 months
(i) under Plan A;
(ii) under Plan B.
11. $1000 is invested at the beginning of each year for 10 years. The rate of interest is fixed at 7.5% per annum. Interest is compounded annually. Calculate, giving your answers to the nearest dollar
(a) how much the first $1000 is worth at the end of the ten years; (b) the total value of the investments at the end of the ten years.
12. Let log10P = x , log10Q = y and log10R = z. Express in terms of x , y and z.
13. Each day a runner trains for a 10 km race. On the first day