Step-by-step explanation:
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Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
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The 20th term is f(20):
f(20) = 20^2 +1 = 401
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<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
5.9 • 10^4
just add the two numbers because the exponents are equal.
Using the equation of the proportional relationship:
Average rate of speed = 60
Time taken to go 300 miles = 5 hrs
Distance travelled in 2.5 hrs = 150 miles
<h3>What is a Equation of a Proportional Relationship?</h3>
A equation of a proportional relationship models the relationship between two variables, x and y, that has a constant of k. It is expressed as y = kx.
Given the following:
Equation: d = 60t
d = distance in miles
t = time in hours
Average rate of speed for the bus = k = 60
Time (t) it would take to go 300 miles (d):
300 = 60(t)
300/60 = t
t = 5 hours
Distance (d) it would travel in 2.5 hours (t):
d = 60(2.5)
d = 150 miles
Learn more about the equation of a proportional relationship on:
brainly.com/question/6869319
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