The nth term

A linear sequence starts 2 5 8 11

Work out the position of the term that is the first to have a value greater than 500

The 5th term in sequence A is also a term in sequence B.

Work out the position of the term in sequence B.

The first four terms of a quadratic sequence are

–1 11 31 59

Work out an expression for the n th term. Give your answer in the form an² + b where a and b are constants.

The nth term of a quadratic sequence is an² – 5n + c where a and c are integers. The first four terms of the sequence are

2 x 16 y

Work out the values of x and y.

Here is some information about three linear sequences, A, B and C.

n th term of C = n th term of A + n th term of B

The n th term of C is 42 – 3 n The first four terms of B are 14 22 30 38

Work out the 20th term of A.

The first four terms of a linear sequence are

15 18.5 22 25.5

Work out an expression for the n th term.

A different linear sequence has n th term 318 – 9 n

Work out the value of the first negative term in the sequence.

A quadratic sequence starts – 2 – 1 4 13

Work out an expression for the n th term.

A different quadratic sequence has nth term n² + 10n

Use an algebraic method to work out how many terms in the sequence are less than 2000 Do not use trial and improvement. You must show your working.

One term in the sequence is

Work out the value of n.

Write down the limiting value of the sequence as n →

Work out an expression, in terms of k, for the 4th term. Give your answer in its simplest form.

The 100th term of the sequence is 525

Work out the value of k.

A term of the sequence has a value of 5

Work out the value of n.

Write down the limiting value of the sequence as n →

The first four terms of a quadratic sequence are

0 1 0 – 3

Work out an expression for the n th term.