Modelling with Sequences & Series (AQA A-Level Mathematics): Quizzes

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Modelling with Sequences & Series
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What is the constant difference between consecutive terms in an arithmetic sequence called?

Common difference

In a geometric sequence, what is the constant multiplier between consecutive terms called?

Common ratio

What is the general form for the nnth term of an arithmetic sequence?

an=a1+(n1)da_n = a_1 + (n-1)d

What is the general form for the nnth term of a geometric sequence?

an=a1rn1a_n = a_1 r^{n-1}

Which formula gives the sum of the first nn terms of an arithmetic sequence?

Sn=n2(2a1+(n1)d)S_n = \frac{n}{2}(2a_1 + (n-1)d)

For what condition does the sum to infinity of a geometric sequence exist?

r<1|r| < 1

A bacteria population of 100 doubles every hour. What is the population after 6 hours?

6400

You save £100 in month 1, then increase by £10 each month. What type of sequence is this?

Arithmetic sequence

A company gives £2000 bonus in year 1, increasing by £500 yearly. Total over 10 years?

£42,500

What is the formula for the sum of the first nn terms of a geometric sequence?

Sn=a1(1rn)1rS_n = \frac{a_1(1-r^n)}{1-r}

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