Pre-Calculus 11 Week 1 – Arithmetic Sequences | Alex's Very Professional Blog

First week of Pre-Calc 11! This week, I learned about Arithmetic Sequences.

Arithmetic sequences are like patterns, they look something like this: 5, 7, 9, 11, 13….

For a pattern to be an arithmetic sequence, all the numbers must have a common difference between them all. The common difference is how much it goes up or down. For our pattern here, the common difference is 2! You see how the pattern continues to increase by 2? This is an arithmetic sequence.

If you wanted to find the 20th term in that pattern, you would use the following formula:

$t_10=t_1+9d$

$t_10 = 5 + 9(2)$

$t_10 = 5 + 18$

$t_10 = 23$

With this formula, we’re saying that we’re going to take the first term in the arithmetic sequence, add the common difference (2) NINE times to get the 10th term. Let’s count it, and make sure my work is correct.

5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Look at that, the 10th term really is 23! For this formula, you don’t have to use t1. You can use any term you already have. If we only had t4, the formula would look like this:

$t_10=t4+6d$

$23 = 11 + 6(2)$

$23= 11 + 12$

$23 = 23$

You can find a general formula for tn as well. It looks like this” $latex t_n = t1 + (n-1)d For example:

$t_23 = 5 + (23-1)d$

$t_23 = 5 + (22)2$

$t_23 = 5 + 44$

$t_23 = 49$

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