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SVEN [57.7K]
3 years ago
7

Write a recursive formula for the sequence below. Use the variable "n" for your formula in your answer.

Mathematics
2 answers:
Brilliant_brown [7]3 years ago
6 0

Answer:

\begin{cases}a_1 = 2\\\\a_{n} = -4*a_{n-1}\end{cases}

============================================

Explanation:

The first line of the answer says "the first term is 2".

The second line says "take any term and multiply by -4 to get the next term".

The a_n represents the nth term while a_{n-1} is the term just before it.

The second line shown above is the same as writing a_{n+1} = -4*a_n

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

The -4 is found by dividing any term over its previous one

-8/2 = -4

32/(-8) = -4

-128/32 = -4

512/(-128) = -4

This shows the common ratio is -4 and this sequence is geometric.

Anika [276]3 years ago
5 0
What huh who?








how do u know huh?
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Step-by-step explanation:

Substitute the y in the 1st equation with the 2nd equation.

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A riverboat travels 54 km downstream in 2 hours. It travels 57 km upstream in 3 hours. Find the speed of the boat and the speed
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Now let's define the variables we will be using:

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When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:

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Then our system of equations is:

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To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:

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Now we can solve this for R:

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Now that we know the value of R, we can use:

B = 19 km/h + R  = 19 km/h + 4km/h = 23 km/h

So the boat's speed is 23km/h and the river's speed is 4km/h.

If you want to learn more, you can read:

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