Answer:
![a_n=a_{n-1}+2^{n-1}\ \ n>1](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%2B2%5E%7Bn-1%7D%5C%20%5C%20n%3E1)
Step-by-step explanation:
Recursive Sequence
We are given the following sequence:
-1, 1, 5, 13...
It's required to find the recursive term for the sequence.
A recursive formula calculates each term as a function of one or more previous terms.
To find the recursive formula, we must find a pattern and transform it into a math expression.
Let's write the sequence, and below it, the difference of consecutive terms:
-1, 1, 5, 13...
+2, +4, +8
Note the difference between consecutive terms is always a power of 2, starting from 2^1, 2^2, 2^3.
The exponent is one less than the number of the term, thus:
![a_n-a_{n-1}=2^{n-1}](https://tex.z-dn.net/?f=a_n-a_%7Bn-1%7D%3D2%5E%7Bn-1%7D)
Thus:
![\mathbf{a_n=a_{n-1}+2^{n-1}\ \ n>1}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_n%3Da_%7Bn-1%7D%2B2%5E%7Bn-1%7D%5C%20%5C%20n%3E1%7D)
Testing:
n=1
(given).
n=2
![a_2=a_{1}+2^{2-1}=-1+2^{1}=1](https://tex.z-dn.net/?f=a_2%3Da_%7B1%7D%2B2%5E%7B2-1%7D%3D-1%2B2%5E%7B1%7D%3D1)
n=3
![a_3=a_{2}+2^{3-1}=1+2^{2}=5](https://tex.z-dn.net/?f=a_3%3Da_%7B2%7D%2B2%5E%7B3-1%7D%3D1%2B2%5E%7B2%7D%3D5)
n=4
![a_4=a_{3}+2^{4-1}=5+2^{3}=13](https://tex.z-dn.net/?f=a_4%3Da_%7B3%7D%2B2%5E%7B4-1%7D%3D5%2B2%5E%7B3%7D%3D13)
8y+10
if the fabric = 30 and yards = y then you would put 8(30) + 10 and you would multiply 8 and 30 and get 240.
Asnwer
8y+10
8(30) +10
240 +10
250
Answer:
thh
Step-by-step explanation:
<span>Perimeter is the measure of distance around a shape.
Area is a measure of the amount of surface something covers</span>