What is the explicit formula for the sequence 10, 15, 22.5, 33.75, …?
1 answer:
Answer:
Step-by-step explanation:
Since there's no one one number you can add to one number in the sequence to get to the next number, this is not arithmetic. It must be geometric. We need then to find the common ratio. Let's start with the first 2 numbers, find a ratio, and then use it to test for accuracy.
10x = 15 and
x = If this is in fact a geometric sequence witha common ratio of 3/2, we should be able to multiply 15 by 3/2 to get to the next number in the sequence. Let's try it out:
Good. So the common ratio is 3/2. The formula for an explicit geometric formula is
where a1 is the first number in the sequence and r is the common ratio. Filling in:
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Well, we are starting with 100 servings, and we're trying to find the amount of ingredients necessary to create 25 servings. To do this, we must first simply divide 25 by 100 to see what the ratio would be, and when we do this, we can see that
25 / 100 =
= 
Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.
In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.
1.) 100 * = 
= 
= 
= 25
2.) 72 * = 
=
= 
= 18
3.) 14 * = 
= 
= 
= 3 
4.) 6 * = 
= 
= 
= <span>1 </span>
5.) 24 * = 
= 
= 
= 6
6.) 80 * = <span>
= 
= 
= <span>20</span>
</span>7.) 50 * = 
= 
= 
= 12
And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)
25 / 100 =
Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.
In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.
1.) 100 *
2.) 72 *
3.) 14 *
4.) 6 *
5.) 24 *
6.) 80 *
</span>7.) 50 *
And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)