Explain how the common difference in an arithmetic sequence is like the slope of a linear function. read more >>
1 answer:
In arithmetic sequence, let the first tern of the arithmetic sequence be, a, and the common difference, d, then the nth term, Tn, of the arithmetic sequence is given by:
For a linear function with y-intercept, c, and slope, m, the linear function is given by:
Comparing the equation of the arithmetic sequence and that of the linear function, we can see that y is compared to Tn, a is compared to c, m is compared to d, and x is compared to n - 1.
Therefore, <span>the common difference in an arithmetic sequence is like the slope of a linear function as both are multiple of a variable.</span>
For a linear function with y-intercept, c, and slope, m, the linear function is given by:
Comparing the equation of the arithmetic sequence and that of the linear function, we can see that y is compared to Tn, a is compared to c, m is compared to d, and x is compared to n - 1.
Therefore, <span>the common difference in an arithmetic sequence is like the slope of a linear function as both are multiple of a variable.</span>
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Answer:
The values of x and y in the diagonals of the parallelogram are x=0 and y=5
Step-by-step explanation:
Given that ABCD is a parallelogram
And segment AC=4x+10
From the figure we have the diagonals AC=3x+y and BD=2x+y
By the property of parallelogram the diagonals are congruent
∴ we can equate the diagonals AC=BD
That is 3x+y=2x+y
3x+y-(2x+y)=2x+y-(2x+y)
3x+y-2x-y=2x+y-2x-y
x+0=0 ( by adding the like terms )
∴ x=0
Given that segment AC=4x+10
Substitute x=0 we have AC=4(0)+10
=0+10
=10
∴ AC=10
Now (3x+y)+(2x+y)=10
5x+2y=10
Substitute x=0, 5(0)+2y=10
2y=10
∴ y=5
∴ the values of x and y are x=0 and y=5