If 6, p and 14 are consecutive terms in arithmetic progression(A.P) Find the value of p
Let first term= a
second term= T2
third term= T3
nth term= Tn
common differnce= d
So, a= 6
T2= P
T3= 14
d= ?
Tn= a + (n - 1)d
T2= a + (2 - 1)d= P
= a + d= P
= 6 + d= P
T3= a + (3 - 1)d= 14
= a + 2d= 14
= 6 + 2d= 14
= 2d= 14 - 6
= 2d= 8
= d= 8/2= 4
= d= 4
Thus, from T2,
6 + d= P (d= 4)
6 + 4= P
10= P
P= 10
I think she meant p = (6+14)/2 = 10
the middle term is the average of the other two.
This is because the difference is constant. That is, p-6 = 14-p
Answer:10
(14 - 6) / 2 = p
Oops! You're right, oobleck!
Well, if 6, p, and 14 are consecutive terms in an arithmetic progression, we can determine the common difference between each term by subtracting consecutive terms.
To find the common difference, we subtract the second term (p) from the first term (6):
6 - p = -p
Next, we subtract the third term (14) from the second term (p):
p - 14 = -d
Since the common difference between consecutive terms is constant, we can set these two equations equal to each other:
-p = p - 14
Now let's solve for p:
-p + p = p - p - 14
0 = -14
Uh-oh! It seems something went wrong in the math. There doesn't seem to be a specific value that satisfies these conditions. Maybe the circus is playing tricks with the arithmetic progression!
To find the value of p in the arithmetic progression (A.P) where 6, p, and 14 are consecutive terms, we need to understand the concept of an arithmetic progression.
In an arithmetic progression, the difference between any two consecutive terms is constant. This constant difference is called the common difference.
Let's denote the first term as a₁, the second term as a₂, the third term as a₃, and so on. The common difference will be represented by 'd'.
So, a₁ = 6, a₂ = p, and a₃ = 14.
To find the value of p, we can use the formula for the nth term of an arithmetic progression:
aₙ = a₁ + (n - 1) * d
Since 6, p, and 14 are consecutive terms, the value of n between them will be 3. Therefore, we can substitute the values into the formula as follows:
a₃ = a₁ + (3 - 1) * d
Plugging in the known values:
14 = 6 + 2d
Now, we can solve this equation to find the value of 'd', which will allow us to determine the value of p.
14 - 6 = 2d
8 = 2d
Divide both sides by 2:
4 = d
Now that we have the value of 'd', we can substitute it back into the original equation to find p:
14 = 6 + 2 * 4
14 = 6 + 8
14 = 14
Therefore, the value of p is 14.