The first three terms of an arithmetic progression are 2x, x+4 and 2x+7 respectively. Find the value of x.
I have no idea where to go from here – any help would be greatly appreciated, thanks in advance!
recall that the terms of an AP have a common difference. That is,
(x+4)-2x = (2x+7)-(x+4)
Now just solve for x, and you're almost done.
Good
Hey there! Don't worry, I've got a riddle for you to lighten things up:
Why don't scientists trust atoms?
Because they make up everything!
Now, let's get back to the arithmetic progression problem. In an arithmetic progression, the common difference between consecutive terms is constant. So, to find the common difference, we can subtract the second term from the first term, and the third term from the second term.
(x + 4) - (2x) = x + 4 - 2x = -x + 4
(2x + 7) - (x + 4) = 2x + 7 - x - 4 = x + 3
Since both of these should be equal, we set them equal to each other:
-x + 4 = x + 3
To solve for x, let's isolate the variable by bringing all the x terms to one side and the constant terms to the other side:
x + x = 4 - 3
2x = 1
Finally, divide both sides by 2 to find the value of x:
x = 1/2
Voila! The value of x is 1/2. I hope that helps, and remember, if you have any more questions, feel free to ask!
To find the value of x in the arithmetic progression, we can set up an equation using the given information.
In an arithmetic progression, the common difference between consecutive terms is constant. Let's find the difference between the second term (x+4) and the first term (2x):
Difference = (x+4) - 2x = -x + 4
Similarly, let's find the difference between the third term (2x+7) and the second term (x+4):
Difference = (2x+7) - (x+4) = x + 3
Since we know that the common difference is the same for both differences, we can set them equal to each other and solve for x:
-x + 4 = x + 3
To solve for x, let's isolate the variable on one side of the equation. First, move the x term to the left side by adding x to both sides:
-x + x + 4 = x + x + 3
4 = 2x + 3
Next, move the constant term to the right side by subtracting 3 from both sides:
4 - 3 = 2x + 3 - 3
1 = 2x
Finally, solve for x by dividing both sides of the equation by 2:
1/2 = (2x)/2
x = 1/2
Therefore, the value of x in the arithmetic progression is 1/2.