Answer: The given series is a geometric series sum 2730.
Step-by-step explanation: We are given to evaluate the following series :
2, 8, 32, 128, 512, 2048.
Let,
denote the n-th term of the given series.
Then, we see the following pattern in the consecutive terms of the given series:
![a_1= 2, \\\\a_2=8=2\times 4=4a_1, \\\\a_3=32=8\times 4=4a_2\\\\a_4=128=32\times4=4a_3,\\\\a_5=2048=128\times4=4a_4,\\\\\vdots~~~~~~\vdots~~~~~~\vdots](https://tex.z-dn.net/?f=a_1%3D%202%2C%20%5C%5C%5C%5Ca_2%3D8%3D2%5Ctimes%204%3D4a_1%2C%20%5C%5C%5C%5Ca_3%3D32%3D8%5Ctimes%204%3D4a_2%5C%5C%5C%5Ca_4%3D128%3D32%5Ctimes4%3D4a_3%2C%5C%5C%5C%5Ca_5%3D2048%3D128%5Ctimes4%3D4a_4%2C%5C%5C%5C%5C%5Cvdots~~~~~~%5Cvdots~~~~~~%5Cvdots)
Therefore, each term after the first one is the product of the preceding term and 4.
That is, the given series is a geometric series with first term 2 and common ratio 4.
Thus, the required sum of the given series is
![S_5\\\\=2+8+32+128+512+2048\\\\=\dfrac{a(r^6-1)}{r-1}\\\\\\=\dfrac{2(4^6-1)}{4-1}\\\\\\=\dfrac{2}{3}\times (4096-1)\\\\=2\times1365\\\\=2730.](https://tex.z-dn.net/?f=S_5%5C%5C%5C%5C%3D2%2B8%2B32%2B128%2B512%2B2048%5C%5C%5C%5C%3D%5Cdfrac%7Ba%28r%5E6-1%29%7D%7Br-1%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B2%284%5E6-1%29%7D%7B4-1%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B2%7D%7B3%7D%5Ctimes%20%284096-1%29%5C%5C%5C%5C%3D2%5Ctimes1365%5C%5C%5C%5C%3D2730.)
The required sum of the series is 2730.
2-3(x+4)=8
2-3x+12=8
2-3x=-4
-3x=-6
x=2
Answer:
the commision of the 3 percent is 6,600.00 i dont fully understand the question if 60 percent is taken from the 3 percent or the 60 is taken from the original.
Step-by-step explanation:
Answer:
X-intercept: (-0.2,0)
Step-by-step explanation:
y=15x+3
I don't know how to show a graph but what you do is start by plotting (0,3) and go up 15 and over 1 to form a line (because the slope is 15).
To find the x-intercept, replace y with 0 and solve for x.
0=15x+3
-3=15x
-3/15
-1/5 (or -0.2)
(-0.2,0)