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

4 minutes 3 marks

Question

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

Hint Hint

Hint

Set up the equations \(u_5 = u_1+4d=11\) and \(u_{12}=u_1+11d=25\) and subtract them to solve for \(d\), then substitute back to find \(u_1\).

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Complete Answer

The common difference is \(d = 2\) and the first term is \(u_1 = 3\).

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Part b

2 minutes 2 marks

Question

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

Hint Hint

Hint

Apply the sum formula \(S_n=\frac{n}{2}(2u_1+(n-1)d)\) using \(u_1 = 3\) and \(d = 2\) with n = 20.

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Complete Answer

The sum of the first 20 terms is \(S_{20} = 440\).

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