Answer: A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)
Step-by-step explanation:
Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.
For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,
a, a+d, a+3d, a+4d...
Notice that each new term keep increasing by a common difference 'd'
The nth term of the sequence Tn will therefore give Tn = a+(n-1)d
If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;
Tn = 14+(n-1)-4 (which gives the required answer)
Tn = 14-4n+4
Tn = 18-4n
Answer:
v(m) = 8 + 48m+ 180m² +216m³
Step-by-step explanation:
Let's first of all represent the edge of the the cube as a function of minutes.
Initially the egde= 2feet
As times elapsed , it increases at the rate of 6 feet per min, that is, for every minute ,there is a 6 feet increase.
Let the the egde be x
X = 2 + 6(m)
Where m represent the minutes elapsed.
So we Al know that the volume of an edge = edge³
but egde = x
V(m) = x³
but x= 2+6(m)
V(m) = (2+6m)³
v(m) = 8 + 48m+ 180m² +216m³
Answer: The probability that the fourth marble Amy picks is black 
The probability that in the fifth attempt she will pick a red or a black marble P(R∩B) =
Step-by-step explanation:
To find the probability that in the fifth attempt she will pick a red or a black marble P(R∩B) .
The total marble in beginning=6+4+8=18
After 3 attempts, the total marbles left=18-3=15
The number of black marbles =8
The probability that the fourth marble Amy picks is black
As four marble has already picked up, then the total marbles left in the box
=18-4=14
Now, as a red marble is already picked in 1st attempt , the number of red marbles in the box now= 4-1=3
And a black marble is already picked in fourth attempt , the number of black marbles in the box now= 8-1=7
Now P(R∩B)=P(R)+P(B)=
