## Acalytica

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Find the first 5 terms of the sequence defined by the formula
$u_{n}=5 n-4 .$
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\begin{aligned} &u_{1}=5 \times 1-4=1 \\ &u_{2}=5 \times 2-4=6 \\ &u_{3}=5 \times 3-4=11 \\ &u_{4}=5 \times 4-4=16 \\ &u_{5}=5 \times 5-4=21 \end{aligned}
So the sequence is
$1,6,11,16,21, \ldots$
Here the terms increase by 5 each time and the formula contains a ' $5 n$ '.
In general, if the terms of a sequence increase by a constant amount, $d$, each time, then the sequence will be defined by the formula
$u_{n}=d n+c$
where $c$ is a constant number.
by Diamond (78,219 points)

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