Given that 3, b, c and 18 are an AP. Find the value of b and c.
What is an AP?
AP = Arithmetric Progression
the 16th term of an AP is 93,given that its common difference is 6.find the 28th term?
To solve this problem, we need to use the arithmetic progression (AP) formula. In an arithmetic progression, each term is obtained by adding a constant difference, denoted by 'd', to the previous term.
Given that 3, b, c, and 18 are an AP, we can set up the following equations:
b - 3 = d -- Equation 1
c - b = d -- Equation 2
18 - c = d -- Equation 3
To find the values of 'b' and 'c', we need to solve these equations simultaneously.
Let's start by solving Equation 1 and Equation 2:
From Equation 1, we have b = d + 3.
Substituting this value of 'b' in Equation 2, we get c - (d + 3) = d, which simplifies to c = 2d + 3.
Now, let's substitute the values of 'b' and 'c' we found into Equation 3:
18 - (2d + 3) = d,
which simplifies to 18 - 2d - 3 = d,
15 - 3 = 2d + d,
12 = 3d,
d = 4.
Now that we know the value of 'd' is 4, we can substitute this back into our equations to find the values of 'b' and 'c' as follows:
b = d + 3 = 4 + 3 = 7,
c = 2d + 3 = 2(4) + 3 = 11.
Therefore, the value of 'b' is 7 and the value of 'c' is 11.