Binomial Distribution

Concept: Geometric distribution:

Step 1: Find .


Step 2: Compute required value.

Step 1: Express the terms of the G.P. in terms of and .
Let the first term of the geometric progression be and the common ratio be . The terms of the G.P. are:
- First term:
- Second term:
- Third term:
We are given that the sum of the first two terms is 12: We are also given that the third term is 16:
Step 2: Solve the system of equations.
From , we can factor out : From , solve for : Substitute into : Now, multiply both sides by to eliminate the denominator: Expanding and simplifying: Rearranging the terms: Dividing by 4:
Step 3: Solve the quadratic equation.
Now, solve the quadratic equation using the quadratic formula: Simplifying: Thus, the two possible solutions for are:
Step 4: Conclusion.
The two possible values for the common ratio are or .