The next term of the sequence is -1.
Given, a sequence is defined recursively by the formula
f(n + 1) = f(n) + 3.
The first term of the sequence is -4.
We, have to find the next term of the sequence,
On using the formula of the sequence, we get
f(n + 1) = f(n) + 3
As, f(1) = -4
Put n = 1,
f(1 + 1) = f(1) + 3
f(2) = f(1) + 3
f(2) = -4 + 3
f(2) = -1
So, the next term of the sequence is -1.
Hence, the next term of the sequence is -1.
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12 - 3 =9 and -5i+4i=1i or i so it is {9-i}
3 2/5 + 4 1/5
3 + 4 = 7
2/5 + 1/5 = 3/5
The answer is 7 3/5
Hope this helps!
The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)
Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1
We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
.. 0 = a*(1 -2)^2 +1
.. 0 = a*1 +1
.. -1 = a
Now we know the equation is
.. y = -(x -2)^2 +1
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If we like, we can expand it to
.. y = -(x^2 -4x +4) +1
.. y = -x^2 +4x -3
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An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
.. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a
.. -1 = a
Then the equation of the graph can be written as
.. y = -(x -1)(x -3)
In expanded form, this is
.. y = -(x^2 -4x +3)
.. y = -x^2 +4x -3 . . . . . . same as above
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