<h3>
Geometric sequence.</h3>
A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).
We have:
![a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots](https://tex.z-dn.net/?f=a_1%3D%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5Ca_2%3D2%5C%5C%5C%5Ca_3%3D8%5C%5C%5C%5Ca_4%3D32%5C%5C%5Cvdots)
Find the common ratio:
![\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}](https://tex.z-dn.net/?f=%5Cboxed%7Br%3D%5Cdfrac%7Ba_n%7D%7Ba_%7Bn-1%7D%7D%7D%5CRightarrow%20r%3D%5Cdfrac%7B2%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cdfrac%7B8%7D%7B2%7D%3D%5Cdfrac%7B32%7D%7B8%7D%3D...%5C%5C%5C%5C%5Cboxed%7Br%3D4%7D)
<h3>The formula of the n-th term of a geometric sequence:</h3>
![\boxed{a_n=a_1\cdot r^{n-1}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D%7D)
Substitute:
![a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}](https://tex.z-dn.net/?f=a_1%3D%5Cdfrac%7B1%7D%7B2%7D%2C%5C%20r%3D4%2C%5C%20n%3D8%5C%5C%5C%5Ca_8%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot4%5E%7B8-1%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot4%5E7%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot16384%5C%5C%5C%5C%5Chuge%5Cboxed%7Ba_8%3D8192%7D)
<h3>Method step by step:</h3>
![a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192](https://tex.z-dn.net/?f=a_4%3D32%2C%5C%20r%3D4%5C%5C%5C%5Ca_5%3Da_4%5Ccdot%20r%5CRightarrow%20a_5%3D32%5Ccdot4%3D128%5C%5C%5C%5Ca_6%3Da_5%5Ccdot%20r%5CRightarrow%20a_6%3D128%5Ccdot4%3D512%5C%5C%5C%5Ca_7%3Da_6%5Ccdot%20r%5CRightarrow%20a_7%3D512%5Ccdot4%3D2048%5C%5C%5C%5Ca_8%3Da_7%5Ccdot%20r%5CRightarrow%20a_8%3D2048%5Ccdot4%3D8192)
Make an equation system based on the problem
eg. a is the first number and b is the seond number
An equation for "<span>The sum of two numbers is 53" is
</span>⇒ a + b = 53
An equation for "<span>twice the first number minus three times the second number is 26"
</span>⇒ 2a - 3b = 26
<span>
Solve the equations by elimination and subtitution method
Eliminate a to find the value of b
a + b = 53 (multiplied by 2)
2a - 3b = 26
--------------------------------------
2a + 2b = 106
2a - 3b = 26
------------------- - (substract)
5b = 80
b = 80/5
b = 16
Subtitute the value of b to one of the equations
a + b = 53
a + 16 = 53
a = 53 - 16
a = 37
The numbers are 16 and 37</span>
Answer:
Angle FGH = Angle JGK
Angle FGJ = Angle KGH
Step-by-step explanation:
Answer: 25% off
Step-by-step explanation:
1= 0.25 + 0.75
25% is off is the equivalency of multiplying the value of the original cost with 0.75.
20*0.75=15
Answer:
the product of 32.56 and 1.4 = 45.584
Step-by-step explanation:
When you multiply decimals, the decimal point is placed in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.
hope i helped:)