The first three terms of a geometric progression are 2^n, 2^n+1, 2^n+2. Find n. ( Answer is 0.5)
n could be any number ... more information is needed
That's all the book has given me. It has given no other information
To find the value of n, we need to solve the equation using the given terms of the geometric progression.
The formula for a geometric progression is:
a₁, a₁*r, a₁*r², a₁*r³, ...
where a₁ is the first term and r is the common ratio.
In this case, the first term is 2ⁿ, and the second term is 2ⁿ⁺¹.
So, we can write the first two terms of the geometric progression as:
2ⁿ, 2ⁿ⁺¹
To find the common ratio, we divide the second term by the first term:
(2ⁿ⁺¹) / (2ⁿ) = 2
Simplifying the expression on the left side, we can rewrite it as:
2^(n+1) / 2ⁿ = 2
Now, we can cancel out the common factor of 2 in the numerator and denominator:
2^(n+1 - n) = 2
2¹ = 2
Simplifying further, we get:
2 = 2
Since this equation is true for any value of n, we can conclude that there is no unique solution for n. It can take any value.
Therefore, I'm sorry, but the answer you provided (0.5) is incorrect.