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jekas [21]
3 years ago
13

A sequence is defined by

Mathematics
2 answers:
garik1379 [7]3 years ago
5 0
I believe the answer is D.

3^2 is 9 and 4^2 is 16, and because 9/16 was the third term in the sequence, you raise both the numerator and the denominator by the number of the term minus 1.

So to find the seventh term, you raise the numerator and denominator by 7 - 1 = 6.

So the answer is 729/4096
uranmaximum [27]3 years ago
3 0
Since each term is -3/4 times the previous term we know that this is a geometric sequence with a common ratio of -3/4.  Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number

Since we do know the common ratio is -3/4 and that a(3)=9/16 we can find the value of a, the initial term.

9/16=a(-3/4)^2

9/16=9a/16

1=a, so the initial term is 1 so now we have the formula for our geometric sequence.

a(n)=1*(-3/4)^(n-1)

a(n)=(-3/4)^(n-1)  so the 7th term is:

a(7)=(-3/4)^6

a(7)=729/4096
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Solution:

First i'm going to divide the graph into 3 parts. Linear, Quadratic and Horizontal graph.

<u>Linear:</u>

Slope=\frac{-2-0}{-4-(-2)}=1\\y=m(x-xo)+yo\\y=1x-(-2)+(-4)\\y=x-2 , x\leq-1

<u>Quadratic:</u>

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<u>Horizontal:</u>

f(x)=7,x\geq 6

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f(x)=x-2 , x\leq-1\\f(x)=(x-2)^{2}-7,-1\leq x\geq 6\\f(x)=7,x\geq 6

<em>Hope this was helpful.</em>

8 0
3 years ago
HELPPP?!!! What is the value of f(-2) and f(3)
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Step #1 for both: figure out which interval your x-value fits into.
For f(-2), x=-2 and -2 fits with x ≤ -2, the top interval.
For f(3), x=3 and 3 fits into -2 < x ≤ 3, the middle interval.

Step #2 for both, plug in your x-value to the piece of the function that fits with that interval.
For f(-2), we know x≤-2, so we use 2x+8 to evaluate x=-2.
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f(-2) = 2(-2)+8 = -4+8 = 4

f(3) = (3)^2 -3 = 9-3 = 6
3 0
2 years ago
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