What is the next term in the arithmetic sequence x+1, 2x-3, x+5?
In an arithmetic sequence, difference between successive terms is the same:(2x-3)-(x+1) = (x+5)-(2x-3) x - 4 = -x + 8 2x = 12 x = 6x + 1 = 7 2x - 3 = 9 x + 5 = 11Next term = 13If you want to write this in terms of x, then we notice a pattern in 1st and 3rd terms: x+1, x+5. These differ by 4. So then 2nd and 4th terms should also differ by 4: 2x-3, 2x+1Next term: 2x+1Sequence: x+1, 2x-3, x+5, 2x+1, x+9, 2x+5, x+13, 2x+9, …
Select the difference 3/2x-1 - 5/2x-1?
Presuming that the (2x - 1) are in the denominators in both fractions, you just have to subtract the numerators. (3 - 5) / (2x - 1) -2 / (2x - 1) The answer is #2.
How would I find the consecutive terms of an arithmetic sequence?
If they are consecutive terms of an arithmetic sequence that means the difference between x+3 and 2x+1 is the same as the difference between 2x+1 and 5x+2. In other words, (5x+2) - (2x+1) = (2x+1) - (x+3). Let's solve this equation, doing so will give the value of x. (5x+2) - (2x+1) = (2x+1) - (x+3). Drop the brackets: 5x + 2 - 2x - 1 = 2x +1 - x - 3 Simplifying both sides of the equation: 3x + 1 = x - 2 Adding 2 to both sides of the equation, 3x + 3 = x. Subtracting 3x from both sides of the equation, -2x = 3, and dividing through by -2 yields x = -1.5, Let's check if these are indeed three consecutive terms of an arithmetic sequence: x + 3 = -1.5 + 3 = 1.5 2x + 1 = 2*-1.5 + 1 = -3 + 1 = -2. 5x + 2 = 5*-1.5 + 2 = -7.5 + 2 = -5.5 Note that -2 - 1.5 = -3.5 and -5.5 - -2 = -5.5 + 2 = -3.5, so the difference is indeed common, so this is the correct answer.
The first, second, and fourth terms of an arithmetic progression are x+1, 2x-1, and 2x+5. How do I find the value of x, a, and d?
We have x+1, 2x-1, and 2x+5For an ap,>> (2x-1) - (x+1) = (2x+5) - (2x-1)>>> x-2 = 6>>> x= 8If x = 8>>> our a.p is, 8+1, 2(8)-1, 2(8)+59,15, 21:· our first term a and common difference d>>> a= 9 and d= 15–9 = 21-15=6>>> a=9 , d=6, and x=8.Thats it
How does y=2x+3 rearrange itself to (y-5)=(2x-1)?
It doesn’t.If you subtract 3 from both sides you gety-3 = 2xI can subtract 2 from both sidesy-5 = 2x-2Doing algebra properly means performing operations on both sides to preserve equality.
Can someone help with these last few problems I have? It would help out a bunch!?
1 ) Demonstrate at least two different ways how to solve the equation 5^(2x+1)=25 a. 5^(2x+1) = 5^2 2x + 1 = 2 2x = 1 x = 1/2 b ln[5^(2x+1)] = ln 25 (2x + 1) ln 5 = ln 25 2x + 1 = (ln 25) / (ln 5) = 2 2x = 1 x = 1/2 2) Solve 2^x=32 and rewrite this equation in a logarithmic form. log (base 2) 32 = x 3) Provide an example of the product, quotient, and power properties. prod. x^3 (x^5) = x^8 Quot. y^7 / y^2 = y^5 power (a^3)^2 = a^6 4) Analyze the characteristics of exponential and logarithmic functions. Make sure you talk about domain and range. Compare them to other functions. >>>> read in your book, or use google 5) Where in the real world might you find an exponential growth or decay application? Explain why your example fits the mathematical model. again --- read ... book, google .. something