Check the forward differences of the sequence.
If
, then let
be the sequence of first-order differences of
. That is, for n ≥ 1,

so that
.
Let
be the sequence of differences of
,

and we see that this is a constant sequence,
. In other words,
is an arithmetic sequence with common difference between terms of 2. That is,

and we can solve for
in terms of
:



and so on down to

We solve for
in the same way.

Then



and so on down to


Answer:
3 hours and 45 minutes
Step-by-step explanation:
let's assume the tank has a volume of x liters.
let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.
the formula to calculate the time is:
time = volume / speed
If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x
So the time this takes is:
time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.
Answer:
y= -4x+22
Step-by-step explanation:
slope= -4
-6=-4(7)+b
-4x7=-28
-6=-28+b
28-6=22
so the equation would be y= -4x+22
b=y-intercept
mx=slope multiplied by x
Answer:
x=90-22
x=68
as the ray divide the right angle into 2
Answer:
length = 24 meters
Step-by-step explanation:
1. l = 2w
2. P = 2l + 2w
P=72
3. 72 = 2l + 2w
4. Substitute w=l/2 to solve for l
72 = 2l + 2(l/2) ---> 72 = 3L - Divide by 3 on both sides
L= 24 meters