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Luda [366]
3 years ago
10

For the following geometric sequence, find the explicit formula. {1, -3, 9, ...} an = -3 · an - 1 where a1 = 1 an = -3 · an - 1

where a1 = -1 an = -1 · (-3)n - 1 an = (-3)n - 1
Mathematics
2 answers:
goldfiish [28.3K]3 years ago
8 0
{ 1,-3,9...}

an = a1 * r^(n-1)
a1 = first term = 1
r = common ratio = -3

so ur formula is : an = 1 * -3^(n-1)
jeka943 years ago
6 0

Answer:

The correct option is 4.

Step-by-step explanation:

The given geometric sequence is

{1, -3, 9, ...}

Here the first term of the sequence is 1 and the common ratio is

r=\frac{a_2}{a_1}=\frac{-3}{1}=-3

The explicit formula of a geometric sequence is

a_n=ar^{n-1}

In the given geometric sequence a=1 and r=-3.

Substitute a=1 and r=-3 in the above formula.

a_n=(1)(-3)^{n-1}

a_n=(-3)^{n-1}

The explicit formula of given geometric sequence is a_n=(-3)^{n-1}.

Therefore the correct option is 4.

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Answer: You can say that the slope is negative since the graph is decreasing.

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
How many ways are there to choose a committee of 7 people from a group of 10 people?7201208405040?
lyudmila [28]

Answer: 120

---------------------------------------------------------------------------------------

Explanation:

We have seven slots to fill. Let's call the slots A, B, C, D, E, F, G

There are 10 choices for slot A

There are 9 choices for slot B

There are 8 choices for slot C

There are 7 choices for slot D

There are 6 choices for slot E

There are 5 choices for slot F

There are 4 choices for slot G

We count down because each previous slot reduces the pool to choose from. Multiply those values out: 10*9*8*7*6*5*4 = 604800

Now divide that result by 5040. Why 5040? Because this is the number of ways to arrange 7 people within a single grouping. Note how 7! = 7*6*5*4*3*2*1 = 5040. W're dividing because order does not matter for any committee.

So we have 604800/5040 = 120 which is the answer we want

---------------

Side note: We could use the alternate route of the nCr combination formula

nCr = (n!)/(r!*(n-r)!)

where n = 10 and r = 7


5 0
3 years ago
James bought a bag of 12 dinner rolls he used 1/6 of the bag how many dinner rolls did james use?
Ierofanga [76]

Answer:

2 is the answer

Step-by-step explanation:

12 divided by 1 divided by 6 = 2

hope this helps plz mark as brainliest

4 0
3 years ago
A company manufacturing company small solid plastic cubes .They use the expression s3 to find the volume of plastic needed to ma
DanielleElmas [232]
Yes, Luis is correct.
If s is equal to the the side length, then in the problem, s is equal to 8 millimeters. 8 x 3 is equal to 24, which would equate to 24 cubic millimeters.
4 0
3 years ago
How to solve 45y to the second power plus 15y minus 10 ?
Lerok [7]

Answer:

Either y =\frac{-2}{3} or, y =\frac{1}{3}

Step-by-step explanation:

We have to solve the following quadratic equation  

45y² + 15y - 10 =0

Now, dividing both sides with 5 we get, 9y² + 3y -2 =0

Hence, to solve the above equation we have to factorize the left-hand part of the equation.

So, 9y² + 3y - 2 =0

⇒ 9y² +6y -3y -2 =0

⇒ (3y +2) (3y -1 ) =0

⇒ Either (3y +2) =0 or (3y -1) =0

⇒ Either y =\frac{-2}{3} or, y =\frac{1}{3} (Answer)

4 0
3 years ago
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