You can begin on any number you like, just be sure to subtract by 3 for each new term.
Example sequence 1: {12,9,6,3} Sequence 1 equation: a_n=-3n+15
Example sequence 2: {1,-2,-5,-8} Sequence 2 equation: a_n=-3n+4
Practice makes perfect
There are infinitely many possibilities for these sequences, you can begin on any number you like. Just be sure to subtract by 3 for each new term, the only restriction is that the common difference d must be -3. Here are two example sequences:
Example 1:& 12-3 →9-3 →6-3 →3
Example 2:& 1-3 →-2-3 →-5-3 →-8
Let's look at these sequences individually in order to find their equations.
Example 1
The first four terms of the first sequence we will be looking at are: {12,9,6,3}. Here we have a common difference d of -3 and the first term a_1 is 12. Using the general form for an arithmetic sequence, we get:
a_n=a_1+(n-1)d ⇒ a_n=12+(n-1)(-3).
We can rewrite this equation into slope-intercept form to make it easier to solve for other terms.
The first four terms of the second sequence we will be looking at are: {1,-2,-5,-8}. Here we have a common difference d of -3 and the first term a_1 is 1. Using the general form for an arithmetic sequence, we get:
a_n=a_1+(n-1)d ⇒ a_n=1+(n-1)(-3).
We can rewrite this equation into slope-intercept form to make it easier to solve for other terms.
