What is the 8th term of the sequence given by an = 3n-5?
1 answer:
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Answer:
1)
2)
3)
Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:
Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:
Subtract. So, our slope is:
2)
Now, let's use the point-slope form:
We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:
Simplify. So, our point-slope equation is:
3)
Finally, we want to convert this into slope-intercept form. So, let's solve for our y.
On the right, distribute:
Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:
Subtract. So, our slope-intercept equation is:
And we're done!
Rather than carrying out IBP several times, let's establish a more general result. Let
One round of IBP, setting
gives
This is called a power-reduction formula. We could try solving for explicitly, but no need.
is small enough to just expand
as much as we need to.
Finally,
so we end up with
and the antiderivative is