X = 1st number
x + 1 = 2nd number
x + 2 = 3rd number
x + (x + 1) + (x + 2) = 18...combine like terms
3x + 3 = 18
3x = 18 - 3
3x = 15
x = 5
x + 1 = 5 + 1 = 6
x + 2 = 5 + 2 = 7
7 + 6 + 5 = 18
13 + 5 = 18
18 = 18 (correct)
largest number is 7
Answer:
It would be 1,088/1,280
Step-by-step explanation:
The answer is 1,088
Answer: 2/8.
Step-by-step explanation:
When we have this type of problem, the usual way to solve them is trying with known types of sequences.
I will start with the arithmetic sequence, where the difference between any two consecutive terms is a constant. And if we call this difference as D, we will have the recursive relation:
Aₙ = Aₙ₋₁ + D
To check if this sequence is an arithmetic sequence, we can take the first two terms and see the difference:
(5/8 - 3/4) = (5/8 - 6/8) = -1/8.
Now let's do the same, but with the second and third terms:
(1/2 - 5/8) = (4/8 - 5/8) = -1/8
The difference is the same, -1/8.
Now we can use the recursive relationship above and the last given term of the sequence to find the next one:
A₅ = A₄ + (-1/8)
A₅ = 3/8 - 1/8 = 2/8
Then the next fraction in the sequence was 2/8.
First differences are ... 0-7 = -7, -1-0 = -1, 4-(-1) = 5, 15-4 = 11, 32-15 = 17.
Second differences are -1-(-7) = 6, 5-(-1) = 6, 11-5 = 6, 17-11 = 6.
The second differences are constant at 6, so the table values would be best fit by a function that is ...
_____
The degree of the polynomial function corresponds to the level of differences that are constant (when the x-values are evenly spaced).
The quadratic function that matches these values is
... y = 3x² +2x -1
... y = (3x-1)(x+1) . . . . in factored form
16 x8 will be the new lenth!
