Math 10 – week 17

In this week of math we learned about arithmetic sequences

A arithmetic sequence looks like this: 2, 4, 6, 8, 10….
An arithmetic sequence is a like a pattern that the numbers will go up by each time. So, in the sequence above it starts at 2 or as we call it, t_{1}. The numbers go up by +2 each time.

Now imagine if you were doing this pattern and had to find out what t_{21} is but fast, instead of counting +2 each time.

first you will start with this equation: t_{n} = t_{1} + (n – 1)(d). So the way you would insert the numbers you have into this equation is by first putting the t_{n} number you want, which will be 21 for this example. Then you just fill in the whole thing like this: t_{21} = 2 + (21n – 1)(2)

now that you inserted everything you will start to solve it. With the difference in the very back you are actually going to multiply it into the numbers in front of it.

t_{21} = 2 + 42 – 2
t_{21} = 42

And your done!

 

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