term given by x+2,3x-1,and 4x-1 form an arithmetic sequence. find the value of x.
i didn't get it how to start this question and how it forms arithmetic sequence?
x+2,3x-1,4x-1 find x A1=x+1,A2=3x-1,A3=4x-1 soln. A2-A1=A3-A2 (3x-1)-(x+2)=(4x-1)-(3x-1) , 2x+1=x,x=-1 so:the sequence is 1,-4,--5 if x=-1 substituted
Whoa, we're talking about an arithmetic sequence here. It's as simple as a clown juggling balls! In an arithmetic sequence, each term is obtained by adding the same number, called the common difference, to the previous term. So let's see if we can connect the dots.
We have three terms here: x+2, 3x-1, and 4x-1. To check if they form an arithmetic sequence, we need to see if the common difference is the same between each pair of consecutive terms.
First, let's look at the difference between the second term (3x-1) and the first term (x+2): (3x-1) - (x+2). Simplifying, we get 2x-3.
Next, let's check the difference between the third term (4x-1) and the second term (3x-1): (4x-1) - (3x-1). Simplifying again, we have x.
Now, if the common difference between the terms is the same, these two results should be equal. So we equate them:
2x-3 = x
Solving this equation, we find:
2x - x = 3
x = 3
Voila! The value of x is 3. We've solved the puzzle and found our answer. Keep those arithmetic balls rolling!
To determine whether the terms x+2, 3x-1, and 4x-1 form an arithmetic sequence, we need to check if the difference between any two consecutive terms is constant.
We'll start by finding the difference between the second and first terms. The second term is 3x-1, and the first term is x+2. Therefore, the difference between the second and first terms is:
(3x - 1) - (x + 2) = 3x - 1 - x - 2 = 2x - 3.
Now, let's find the difference between the third and second terms. The third term is 4x-1, and the second term is 3x-1. Thus, the difference between the third and second terms is:
(4x - 1) - (3x - 1) = 4x - 1 - 3x + 1 = x.
If the terms form an arithmetic sequence, the differences should be the same. In this case, we have:
Difference between 2nd and 1st terms: 2x - 3,
Difference between 3rd and 2nd terms: x.
Since these two differences are not the same, the terms x+2, 3x-1, and 4x-1 do not form an arithmetic sequence.
Therefore, we cannot determine a specific value of x based on this information.
To determine if the terms - given by x+2, 3x-1, and 4x-1 - form an arithmetic sequence, we need to check if there is a common difference between the terms.
In an arithmetic sequence, each term is obtained by adding a fixed value to the previous term. If we subtract any two consecutive terms and the result is always the same, then the sequence is arithmetic.
Let's find the differences between the terms:
The difference between the second term and the first term can be found by subtracting the first term from the second term:
(3x-1) - (x+2) = 2x - 3.
Similarly, the difference between the third term and the second term can be found by subtracting the second term from the third term:
(4x-1) - (3x-1) = x.
Now we have two differences: 2x - 3 and x.
To form an arithmetic sequence, these differences should be equal, meaning that 2x - 3 = x.
Solving this equation will give us the value of x.
Let's solve it step by step:
2x - 3 = x.
First, we need to isolate the variable, which means getting the x term on one side of the equation:
2x - x = 3.
The x term can be canceled out since it appears on both sides:
x = 3.
Therefore, the value of x is 3.