Advanced problem solving with further sequences | Maths

Starter quiz

Interest which is calculated on the original amount and the interest accumulated over the previous period is called ______ interest.

'compound' ✓
If a geometric sequence starts 75, 105, 147, ... what is the common ratio? Give your answer as a decimal.

'1.4' ✓
£100 is invested at 1% compound interest a month. Which calculation would find the value of the money after 5 months?

$100 \times 5(1.01)$

$100 \times 5(1.1)$

$100 \times 1.01^5$ ✓

$100 \times 1.1^5$
Which of these are examples of exponential equations?

$y=x^2$

$y=100x^3$

$y=2^x$ ✓

$y = 3 \times 5^x$ ✓

$y= x^{1\over 2}$
Which of these is the general form for an odd number when $n$ is an integer?

$n$

$n+1$

$2n$

$2n +1$ ✓

$3n$
What is the $n^\text{th}$ term of the quadratic sequence which starts 1, 3, 9, 19, 33, ...?

$n^2 -1$

$2n^2 -4n +3$ ✓

$2n^2+4n-3$

$4n^2 -10n + 7$

$4n^2 -2n-1$

£1600 is borrowed with yearly compound interest and after a year £2240 is owed. What is the yearly interest rate?

1.4%

14%

25%

30%

40% ✓
A loans company charges 4% interest a month. If £35 152 was owed after three months, how much was borrowed?

'£31 250' ✓
£40 000 was borrowed with compound interest and after 4 years £58 564 was owed. What was the yearly interest rate? Assume no repayments were made.

10% ✓

14%

37%

45%

50%
£24 000 is borrowed at a compound interest rate of 5% a month. What would be the $n^\text{th}$ term rule for the geometric sequence formed from the amount owed each month starting with month 1?

$24 000n + 1.05$

$1.05n + 24 000$

$24000 \times n^{1.05}$

$24 000 \times 1.05^n$ ✓
Some money was borrowed with compound interest. After 2 years £4000 was owed and after 4 years £6250 was owed. After how many years would the loan value be greater than £10 000 ?

'7' ✓
Which of these is the $n^\text{th}$ term rule for the triangular numbers? (1, 3, 6, 10, 15, ...)

$n^2 -n$

$\frac{n(n+1)}{2}$ ✓

$\frac{n^2-(n-1)}{2}$

$\frac{1}{2}n^2 -\frac{1}{2}n + \frac{1}{2}$

$\frac{1}{2}n^2 +\frac{1}{2}n$ ✓

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Compound interest can be thought of as a geometric sequence.
You can apply your knowledge of geometric sequences to solve algebraic compound interest problems.

A multiplier of 1.3 is used to increase a value by 3%

A multiplier of 1.3 is used to increase a value by 30%

Interest - Interest is money added to savings or loans.
Compound interest - Compound interest is calculated on the original amount and the interest accumulated over the previous period.
Exponential - The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.