Using the recurrence relation, we can find a couple more values in the sequence:
- a3 = 3a2 -3a1 +a0 = 3(4) -3(2) +2 = 8
- a4 = 3a3 -3a2 +a1 = 3(8) -3(4) +2 = 14
First differences are 0, 2, 4, 6, ...
Second differences are constant at 2, so the function is quadratic.
The sequence can be described by the quadratic ...
... an = n² -n +2
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We know the value for n=0 is 2, so we can find <em>a</em> and <em>b</em> using the given values for a1 and a2.
... an = an² +bn +2
... a1 = 2 = a·1² +b·1 +2 . . . . for n=1
... a + b = 0
... a2 = 4 = a·2² -a·2 +2 . . . . for n = 2; using b=-a from the previous equation
... 2 = 2a
... a = 1 . . . . so b = -1
Answer:
5.3333333333
Step-by-step explanation:
A number is called a rational if it can be written in the form of p/q where p/q are integers and q≠0.
The terminating numbers are always a rational number.
The number 5.3333333... is a rational number.
Answer:
Add 7 black beads
Step-by-step explanation:
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (<em>b</em> meaning black) b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
<u>We need 9 black beads in total</u>.
Check answer
9 : 3 Both sides divisible by 3; reduce ratio
= 3 : 1 Correct ratio
There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore we need to add 7 black beads.
Answer:
$2
Step-by-step explanation:
40 x 0.05 = 2
Answer:
The length of the rectangular pen is 40ft. The width of the rectangular pen is 20ft
