Write an equation for the nth term of the arithmetic sequence. 2, 5, 8, 11, ...
1 answer:
Answer:
An equation for the nth term of the arithmetic sequence.
Step-by-step explanation:
Given the sequence
2,5,8,11,...
An arithmetic sequence has a constant difference 'd' and is defined by
here
- a₁ = 2
computing the differences of all the adjacent terms
- d = 5-2 = 3, d = 8-5=3, d=11-8=3
Using the nth term formula
substituting a₁ = 2, d = 3
Thus, an equation for the nth term of the arithmetic sequence.
You might be interested in
You can find the slope either by just looking at the line or using the slope formula.
#1: The slope formula is:
Find two points and plug it into the formula
I will use (0, 2) and (1, -1)
(0, 2) = (x₁, y₁)
(1, -1) = (x₂, y₂)
[two negatives cancel each other out and become positive]
m = -3
#2: To find the slope without having to do the work, you use this:
Rise is the number of units you go up(+) or down(-) from each point
Run is the number of units you go to the right from each point
If we start at a defined/obvious point, like (0, 2), find the next point and see how many units it goes up or down and to the right. The next point is (1, -1), so from each point, you go down 3 units and to the right 1 unit. So your slope is -3/1 or -3. You can make sure the slope is right by looking at another point.