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:
8 cm
Step-by-step explanation:
4+4=8 To get the diameter, double the radius and add them together.
Answer:
22.5
Step-by-step explanation:
125
x 18
---------
1. first set up your problem
2 4
125
x 18
------
1000
2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.
3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.
4. multiply 8 by 1 getting 8 then add the 2 above the 1 to 8 getting 10. Then put the ten infront of the tw zeros. 1000
125
x 18
--------
1000
0
Next add a 0 as a place filler under the 0 at the end.
125
x 18
-------
1000
1250
Then multiply the 1 by 5, then 1 by 2, then finnaly 1 by 1, getting you 1250.
1000
+1250
add together
getting 2250
then move 2 decimal places over to get 22.5
An equivalent expression would be 2x+4
