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ahrayia [7]
3 years ago
6

Write an explicit formula for a^n the nth term of the sequence 1,3,9....

Mathematics
1 answer:
frutty [35]3 years ago
7 0

Answer:

  a_n = 3^(n -1)

Step-by-step explanation:

The n-th term of a geometric sequence with first term a1 and common ratio r is given by ...

  a_n = a1·r^(n-1)

Your sequence has first term 1 and ratio r=3, so the sequence is given by ...

  a_n = 3^(n -1)

_____

<em>Comment on sequences and series</em>

The sequences we commonly study are "arithmetic" and "geometric." Each of these has an explicit formula for the n-th term, based on the first term and the common difference or ratio. Similarly, each series (sum of terms of a sequence) also has a formula. That's 4 formulas to keep track of; not difficult. One of them, the formula for the n-th term of a geometric sequence, is shown above.

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Is 0 an integer ?<br> It wont let me post without making it longer
lina2011 [118]

Yes, it is. You may prove it using something like this: 1 is an integer. 1-1 is a difference between integers. A difference between integers returns an integer, so 0 is an integer.

7 0
2 years ago
Jacob transformed quadrilateral FGHJ to F'G'H'J'.
Rudik [331]

Answer:

A. Reflection across the line x = 1

Step-by-step explanation:  

Please find the attachment.

We have been given that Jacob transformed quadrilateral FGHJ to F'G'H'J'.  We are asked to find which transformation Jacob used to reflect FGHJ to F'G'H'J'.

Since we know that while reflecting a figure, the line of reflection will lie between the original figure and reflected figure. Each point of the reflected figure will have the same distance from the line of reflection as the corresponding point of the original figure.              

Now let us see our given choices one by one.

A. Reflection across the line x = 1.

Upon looking at point G and G' we can see that both points are equidistant (2 units) from the line x=1. Other corresponding points of both quadrilaterals are also equidistant from line x=1, therefore, Jacob used the reflection across the line x=1 to transform quadrilateral FGHJ to F'G'H'J'.

B. Reflection across the line y = 1 .      

If Jacob had reflected quadrilateral across line y=1, the points of quadrilateral F'G'H'J' will lie in second and third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option B is not a correct choice.

C. Reflection across the line y-axis.

If Jacob had reflected quadrilateral across y-axis, the coordinates of points of quadrilateral F'G'H'J' will be G'(1,4), H'(1,2), J'(4,0) and F'(2,5). Therefore, option B is not a correct choice.

D.  Reflection across the x -axis.

If Jacob had reflected quadrilateral across x-axis, the points of quadrilateral F'G'H'J' will lie in third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option D is not a correct choice.

3 0
3 years ago
Need help with number 22
Serga [27]
The sums range from 2 to 12 of which 6 are even out of 11 possible sums.
There are 4 multiples of 3, two of which are odd.

So the number of even sums is 6 and there are 2 unique or odd multiples of 3.

So there are a total 6+2=8 outcomes we want out of 36 possible outcomes.

The probability is then 8/36 or 2/9
4 0
3 years ago
Yoku Is putting on sunscreen. He uses 2 ml to cover 50 cm² of his skin. He wants to know how many milliliters of sunscreen he ne
Temka [501]
Alright so here it is

325/50=6.5
6.5*2=13
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Anvisha [2.4K]

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