Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple for- mula or rule.

A sequence can be arithmetic, geometric or neither

The first three terms are given as:

3, 5, 7

The above terms have a common difference of 2.

So, the first sequence is f(n) = 1 + 2n

Another rule is to subtract a term from the product of 4 and the previous term.

So, we have: f(n+2) = 4f(n) - f(n + 1)

Also, we can subtract a 8 from the product of consecutive terms.

So, we have: f(n+2) = f(n) * f(n + 1) - 8

Read more about sequence and series at:

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1. Perhaps the simplest rule is one that makes this the start of an arithmetic sequence:

Then the sequence will continue ...

... 3, 5, 7, 9, 11, 13, 15, ...

2. We can multiply the two terms by some values, add the results, then add some constant. There are an infinite number of ways to choose such values. Here's one set of numbers that give the third term from the first two:

Then the sequence will continue ...

... 3, 5, 7, 13, 15, 37, 23, ...

3. We can multiply adjacent values and add a constant.

Then the sequence will continue ...

... 3, 5, 7, 28, 188, 5256, 988120, ...

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

18.75 gallons

step-by-step explanation: