An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.

Conditions in arithmetic sequences

Maths

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

Further sequences

$$5n-28=100$$ is __________ we can solve in order to help us find the first term over $$100$$

Using trial and error, which is the best estimate at which to start to find the first value over $$1000$$ in the sequence starting $$-17,-13,-9,-5,-1, ...$$?

If you open a savings account with $$£50$$ and put $$£8$$ a week in to the account every week thereafter without withdrawing anything, after how many weeks will you reach $$£200$$?

Which term is the first value below $$−300$$ in the arithmetic sequence starting $$91, 83, 75, 67, 59, …$$?

The $$58^\text{th}$$ term is above $$98$$

The $$59^\text{th}$$ term is above $$98$$

The solution to $$2n-19=98$$ is $$n=58.5$$ What does this tell us about this sequence? $$-17,-15,-13,-11, ...$$

What is the last positive value in the sequence $$380, 365, 350, 335, ...$$?

$$6n-7$$ is the __________ of the arithmetic sequence starting $$-1, 5, 11, 17, 23, ...$$

What is the $$n^\text{th}$$ term rule of the sequence $$14,22,30,38,46, ...$$?

What is the $$n^\text{th}$$ term rule of the sequence $$197,191,185,179,173, ...$$?

What is the $$40^\text{th}$$ term of the sequence $$9n+51$$?

What position is $$213$$ in the following arithmetic sequence? $$18,23,28,33, ...$$

Solve the equation $$8n-37=495$$ If necessary leave your answer as a decimal.  $$n=$${{}}

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