Sequences and series

Sequences and series can appear in many different forms on Paper 1. They have appeared in both Section A and Section B in the past. Also, the applications of them have been asked, including financial applications.

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Students need to be able to recognise a sequence and identify the type of sequence being used. Be familiar with arithmetic and geometric sequences and series and the

Tn and formulae for these sequences. They

Sn are on page 22 of the log tables. ●

You need to know how to calculate the for Tn a quadratic sequence. Example: Find for the sequence 3,5,9,15,… Tn

The second change is constant therefore the sequence is quadratic. So is of the form Tn an2+ bn + c where a equals half the second change. Solve these simultaneous equations to find that b = –1, c =3

⇒Tn

= n2 – n +3

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You also need to solve problems involving infinite geometric series.

Example: Find the sum to infinity for the sequence For this sequence, ●

You need to be able to apply your knowledge to problems involving recurring decimals Example: Write 0.3 as a fraction, using the sum of a geometric series. This is an infinite geometric series with ●

Be able to derive the formula for the sum to infinity of geometric series by considering the limit of a sequence of partial sums