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
Answer:-9/2 or -4.
5
Step-by-step explanation:
Answer:
$5
Step-by-step explanation:
Let the cost of one burger be $b while the cost of one small fries be s
2 burgers and 2 small fries cost $14
This means that;
2b + 2s = 14
divide both sides by 2
b + s = 7 •••••••• (i)
Three burgers and four small fries cost $23
Mathematically;
3b + 4s = 23 •••••••• (ii)
From i , we can see that s = 7- b
we can now substitute this into equation ii
3b + 4(7-b) = 23
3b + 28 -4b = 23
4b -3b = 28 -23
b = $5
one burger costs $5
In quadrant 2 is where it lies.
Answer:
x - 5
Step-by-step explanation:
