Given that 4,p,13 are Consecutive terms of an A. P, find tbe value of P and Q.
To find the value of P and Q, we need to use the formula for the nth term of an arithmetic progression.
The formula for the nth term of an arithmetic progression is given by:
nth term = first term + (n-1) * common difference
In this case, we are given that 4, p, and 13 are consecutive terms of an arithmetic progression. Let's assume that 4 is the first term, p is the second term, and 13 is the third term.
Using the formula, we can write the equations:
p = 4 + (2-1) * common difference
13 = 4 + (3-1) * common difference
Simplifying these equations, we have:
p = 4 + common difference
13 = 4 + 2 * common difference
From the first equation, we can solve for the common difference:
common difference = p - 4
Substituting this into the second equation, we have:
13 = 4 + 2 * (p - 4)
13 = 4 + 2p - 8
13 = 2p - 4
2p = 17
p = 8.5
Therefore, the value of P is 8.5.
To find the common difference (Q), we can substitute the value of P into the first equation:
p = 4 + common difference
8.5 = 4 + common difference
common difference = 8.5 - 4
common difference = 4.5
Therefore, the value of Q is 4.5.