If the 1st,2nd,3rd term of a G.P areX,X+1,X+4 respectively,find X
a = X
a r = X+1
so
r = (X+1)/X
a r^2 = X+4
so
X [(X+1)/X ]^2 = X + 4
(1/X)(X^2 + 2 X + 1) = X + 4
X^2 + 2 X + 1 = X^2 + 4 X
X = 1/2
To find the value of X in the given geometric progression (G.P), we can use the formula for the nth term of a G.P., which is given by:
An = A1 * r^(n-1)
where An represents the nth term, A1 represents the first term, r represents the common ratio, and n represents the position of the term in the G.P.
Let's use the provided information to solve for X.
Given:
First term (A1) = X
Second term (A2) = X + 1
Third term (A3) = X + 4
Using the formula for the nth term of a G.P., we can set up the following equations:
A2 = A1 * r
X + 1 = X * r ...(Equation 1)
A3 = A2 * r
X + 4 = (X + 1) * r ...(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (X and r). We can solve these equations simultaneously to find the values of X and r.
Let's solve the system of equations to find X.
Step 1: Solve Equation 1 for r:
X + 1 = X * r
r = (X + 1) / X
Step 2: Substitute the value of r in Equation 2:
X + 4 = (X + 1) * [(X + 1) / X]
Simplify the equation:
X + 4 = (X^2 + 2X + 1) / X
Multiply both sides by X to clear the fraction:
X^2 + 4X = X^2 + 2X + 1
Step 3: Rearrange the equation and eliminate X^2:
4X - 2X = 1
2X = 1
X = 1/2
Therefore, the value of X in the given geometric progression is X = 1/2.