Edexcel IGCSE Math A 3.1.C nth term of linear sequences

Practise nth-term questions by finding the common difference, building the expression in n and using it to calculate or reject terms.

Exam points

Find an expression for the nth term of a linear sequence using the common difference.
Use the nth-term expression to calculate a specified term such as the 12th term.
Explain why a number cannot be a term by substituting or solving for n.

[Maximum number: 3]

Here are the first four terms of an arithmetic sequence.

$1\qquad4\qquad7\qquad10$

(a)

Find an expression, in terms of n, for the nth term of this sequence.

[ 2 ]

3n-2

M1 for 3n+k, where $k\ne -2$ , or equivalent.
A1 for 3n-2, or equivalent such as 1+(n-1)3.
Working not required, so a correct answer scores full marks unless from obvious incorrect working.

(b)

The nth term of a different arithmetic sequence is 5n+17.

Find the 12th term of this sequence.

[ 1 ]

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3.1.C nth terms of arithmetic sequences question 1

Question (a)

Question (b)