Week 17 – Math 10 – Arithmetic sequences

This week in Math 10, I have chosen to talk about arithmetic sequences.

A sequence is a repeating pattern of numbers that increase or decrease by an amount. Arithmetic sequences in particular increase or decrease by the same amount, expressed as difference, or the letter d. For example, here is a basic sequence.

3, 6, 9, 12, 15…

For this sequence, d=3. Sequences also have rules, which can be discovered with this equation.

$t_{n}=t_{1}+(n-1)d$

Here, the letter t represents the term (positions in the sequence) and n specifies which term (which position.) $t_{1}$ is term 1 for instance, which in this case is 3. Lets fill in the equation with our information.

$t_{n}=3+(n-1)3$

We now distribute the difference to the n-1 preceding it in the equation.

$t_{n}=3+3n-3$

Now, simplify like terms. The +3 and the -3 cancel each other out, so we’re left with the following.

$t_{n}=3n$

In other words, a term is equal to three times the term position. Here’s a more complex sequence that decreases.

44, 38, 32, 26, 20…

The difference here is -6, and term 1 is 44. Plugging that into the equation…

$t_{n}=44+(n-1)(-6)$ $t_{n}=44-6n+6$ $t_{n}=-6n+50$

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Week 17 – Math 10 – Arithmetic sequences

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