Arithmetic Sequence

00:00 5 marks

An arithmetic sequence has fifth term \(u_5 = 11\) and twelfth term \(u_{12} = 25\).
(a) Find the first term \(u_1\) and the common difference \(d\). [3]
(b) Find the sum of the first 20 terms of the sequence, \(S_{20}\). [2]

Part a

3 minutes 3 marks

Question

Find the first term \(u_1\) and the common difference \(d\). [3]

Hint Hint

Hint

Set up the equations \(u_5 = u_1 + 4d\) and \(u_{12} = u_1 + 11d\) then subtract to eliminate \(u_1\) and solve for d, before finding \(u_1\).

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Complete Answer

\(u_1 = 3\) and \(d = 2\)

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Part b

2 minutes 2 marks

Question

Find the sum of the first 20 terms, \(S_{20}\). [2]

Hint Hint

Hint

Use the sum formula \(S_n = \frac{n}{2}(2u_1 + (n-1)d)\) and substitute \(u_1 = 3\), \(d = 2\), and \(n = 20\).

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Complete Answer

\(S_{20} = 440\)

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