Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
Let's represent our number as x.
x is being added to 6 * x², and it equals 12
Factor:
Solve for x:
Therefore,
x = -3/2 and 4/3.
The linear model of this case takes the form:
y = a(x-b) + k
<span>The cost of having a package delivered has a base fee of $9.70
this is "k" >>>>> k=9.7 (fixed amount of fee)
THEN
</span>
<span>Every pound over 5 lbs cost an additional $0.46 per pound
that means: 0.46(x-5)
in other words, if the package weighs foe example 9 pounds, then 9-5=4, it will cost 0.46*4 for these 4 extra pounds
Finally we have the linear form of this: C = 0.46 (W - 5) + 9.7
</span>
Answer:
3.93700787402, almost 4
Step-by-step explanation:
10 ÷ 2.54
3 × 2.50 = 7.50
3 × 0.04 = 0.12
7.50 + 0.12 = 7.65
7.65 + 2.54 = 10.19
The precise number is use calculator.
