The 2nd,3rd and 4th term of an arithmetic progression are x-1,5,x+2 respectively calculate the value of x.
for your AP,
5 - (x-1) = x+2 - 5
solve for x
Why did the arithmetic progression start going to therapy? Because its terms felt so distant and disconnected!
Now, let's solve this math problem, shall we? Since we have the 2nd, 3rd, and 4th terms of an arithmetic progression, we know that the common difference (d) is the same between each consecutive term.
From the given information, we have:
2nd term (a2) = x - 1
3rd term (a3) = 5
4th term (a4) = x + 2
To find the value of x, let's look at the difference between the 3rd and 2nd terms:
a3 - a2 = 5 - (x - 1)
d = 5 - x + 1
d = 6 - x
Next, let's examine the difference between the 4th and 3rd terms:
a4 - a3 = (x + 2) - 5
d = x + 2 - 5
d = x - 3
Since the common difference (d) is the same between both pairs of terms, we can equate the two equations:
6 - x = x - 3
Now let's solve for x:
6 + 3 = x + x
9 = 2x
x = 4.5
So the value of x is 4.5. However, it's important to note that arithmetic progressions typically have whole number terms. In this case, it seems our progression is not consistent or maybe it ran off into fractions! Keep track of those wily arithmetic progressions!
To find the value of x in this arithmetic progression, we can use the formulas for the nth term of an arithmetic progression and the common difference.
The nth term of an arithmetic progression can be calculated using the formula:
an = a1 + (n - 1)d,
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, given that the second term (a2) is x - 1, the third term (a3) is 5, and the fourth term (a4) is x + 2, we can set up the following equations:
a2 = a1 + d
x - 1 = a1 + d ---(equation 1)
a3 = a1 + 2d
5 = a1 + 2d ---(equation 2)
a4 = a1 + 3d
x + 2 = a1 + 3d ---(equation 3)
Now we have a system of three equations with three variables (x, a1, and d).
Let's solve this system of equations to find the value of x.
To find the value of x in an arithmetic progression given three terms, you can use the property that the common difference between any consecutive terms in an arithmetic progression is constant. Here's how you can solve the problem step by step:
Step 1: Determine the common difference (d)
The common difference (d) is the difference between any two consecutive terms in the arithmetic progression. In this case, we can subtract the second term from the first term, or the third term from the second term. Let's subtract the second term from the first term:
(x - 1) - 5 = x - 6
Step 2: Set up an equation using the common difference
Since the common difference is constant, we can set up an equation using the relationship between the second and third terms:
5 - (x - 1) = (x + 2) - 5
Step 3: Solve the equation
Simplify both sides of the equation:
5 - x + 1 = x + 2 - 5
6 - x = x - 3
Combine like terms:
-x - x = -3 - 6
-2x = -9
Divide both sides of the equation by -2:
x = -9 / -2
x = 9/2
Therefore, the value of x is 9/2 (or 4.5).