What is the 214 term in the sequence 7,10,13,16?
1 answer:
We can figure this out using the explicit formula.
n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.
f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n
Now, we can input 214 for n and solve.
f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646
The 214th term in this sequence is 646.
n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.
f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n
Now, we can input 214 for n and solve.
f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646
The 214th term in this sequence is 646.
You might be interested in
Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
Given the first equation:
You can identify that:
By definition, the line intersects the x-axis when . Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:
Now you can graph it.
Solve for "y" from the second equation:
You can identify that:
Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has<u> Infinitely many solutions.</u>
See the graph attached.
