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:
6
Step-by-step explanation:
I think its 6 times greater because the length was tripled and the width was doubled thus : 3 * 2 = 6
HOPE THIS HELPED
Answer:
D i believe
Step-by-step explanation: hoped this helps
Answer:
36.67 [mile/hour].
Step-by-step explanation:
1) use the formula: V=S/t, where S - entire jorney, v - average speed (required to calculate), t - elapsed entire time.
2) according to the formula above S=50+60=110 miles; t= 50/40 + 1.75=1.25+1.75=3 hours.
3) after the substitutuion 110 and 3 into the formula above:
v=110/3≈36.67 miles/h.
