Given sequence: ![a_n=a_{n-1}+5](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%2B5)
.
We need to find first four terms of the sequence.
We already given first term -3.
Let us find second term
.
Plugging n=2.
![a_2=a_{2-1}+5 = a_1+5= -3+5 = 2.](https://tex.z-dn.net/?f=a_2%3Da_%7B2-1%7D%2B5%20%3D%20a_1%2B5%3D%20-3%2B5%20%3D%202.)
Now taking n=3.
.
Now, n=4.
.
We got terms -3, 2, 7 and 12.
<h3>Therefore, correct option is B) –3, 2, 7, 12.</h3>
5.7 inches is the correct answer
Using a geometric series, it is found that he swims 1897 yards in the first week.
In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.
The general equation of a geometric series is given by:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
In which
is the first term.
The sum of the first n terms is given by:
![S_{n} = \frac{a_1(1 - q^n)}{1 - q}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Ba_1%281%20-%20q%5En%29%7D%7B1%20-%20q%7D)
In this problem:
- 200 yards on the first day, thus
. - Each day, the distance increases by 10%, since 100% + 10% = 110% = 1.1,
. - First week is first 7 days, thus
![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
Then:
![S_{n} = \frac{a_1(1 - q^n)}{1 - q}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Ba_1%281%20-%20q%5En%29%7D%7B1%20-%20q%7D)
![S_{7} = \frac{200(1 - 1.1^7)}{1 - 1.1}](https://tex.z-dn.net/?f=S_%7B7%7D%20%3D%20%5Cfrac%7B200%281%20-%201.1%5E7%29%7D%7B1%20-%201.1%7D)
![S_{7} = 1897](https://tex.z-dn.net/?f=S_%7B7%7D%20%3D%201897)
He swims 1897 yards in the first week.
A similar problem is given at brainly.com/question/23711475
Answer:
![\displaystyle 31\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%2031%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
9 = −1 + 4a
+ 1 + 1
_________
![\displaystyle \frac{10}{4} = \frac{4a}{4} \\ \\ 2\frac{1}{2} = a \\ \\ \\ 3[2\frac{1}{2}] + 4[2\frac{1}{2}] + 9 + 5 = 7\frac{1}{2} + 10 + 9 + 5 = 31\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B10%7D%7B4%7D%20%3D%20%5Cfrac%7B4a%7D%7B4%7D%20%5C%5C%20%5C%5C%202%5Cfrac%7B1%7D%7B2%7D%20%3D%20a%20%5C%5C%20%5C%5C%20%5C%5C%203%5B2%5Cfrac%7B1%7D%7B2%7D%5D%20%2B%204%5B2%5Cfrac%7B1%7D%7B2%7D%5D%20%2B%209%20%2B%205%20%3D%207%5Cfrac%7B1%7D%7B2%7D%20%2B%2010%20%2B%209%20%2B%205%20%3D%2031%5Cfrac%7B1%7D%7B2%7D)
I am joyous to assist you anytime.
Answer:are you saying mx+b
Step-by-step explanation: hopefully that helps you mark me brainlest please
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