Modelling with Sequences & Series (Edexcel 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

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

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

What is the sum of first nn terms formula for an arithmetic sequence?

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

In a geometric sequence, each term is found by what operation on the previous term?

Multiplying by a constant

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

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

What is the sum of first nn terms for a geometric sequence where r1r \neq 1?

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

What condition must be met for a geometric sequence to have a sum to infinity?

r<1|r| < 1

Bacteria double every hour starting with 100. How many bacteria are there after 6 hours?

6400

You save £100 in month 1, increasing £10 monthly. What is saved in month nn?

90+10n90 + 10n

A bonus starts at £2000, rising £500 yearly. What is the total bonus over 10 years?

£42,500

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