Core 2, Key skill 1: Arithmetic and Geometric progressions
Arithmetic
Geometric
Complete the table where possible
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Sequence: GP or AP? (or neither...) |
nth term |
Sum of first 20 terms |
Sum to infinity if possible |
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Problems involving sequences
Remember: identify whether it is an AP or a GP first then
use the formula given.
Problem 1: Jack puts £100 in a bank. It increases at a rate
of 10% every year.
Write down an expression for the nth term
How long before he has more than £1000
Problem 2: Peter receives £10 on day 1, then £14 on day
2, then £18 on day 3...
Write down an expression for the nth term
What is his total after 8 weeks?
How long before he has a total of £3000?
Problem 3: A certain type of insect live for 1 year.
There are 100,000 insects in the first year. The number of insects in the next
year – offspring – will be 40% of the adult population of the previous year.
Write down the first 4 years of this sequence.
Write down an expression for the nth term
How many insects have existed after 10 years?
What is the total number of insects which could ever live?