Let x be the cost of 1 shirt and y be the cost of 1 scarf.
Since, 3 shirts and 2 scarves cost $94, we have,
3x + 2y = 94
Since the number of unknowns is greater than the number of equations (2 > 1), the above system has infinitely many solutions.
If t is the cost of 1 scarf, then
3x + 2t = 94
3x = 94 - 2t
x = 
For different values for t, we will get different values for x.
Set t = 2.
Then, x = 
= 
= 
= 30
So, if the cost of 1 scarf is $2, then the cost of 1 shirt is $30.
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:
x+5/x+3
Step-by-step explanation:
