Find the value of x such that the following sequence forms a geometric progression...?
x-1, 3x+4, 6x+8...so i am suppose to solve this by this rule: a,b,c then b^2=ac but I am just going around in circles because i have no idea how to get an answer, my textbook says the answer is -6, but i want to know the working out...any answers appreciated!
thanks in advance:)
A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a fixed number. This fixed number is called the common ratio, denoted by r.
To find the value of x in a geometric progression, you can use the formula x = a * r^(n-1), where a is the first term, r is the common ratio, and n is the position of the term you are trying to find. Alternatively, you can also use the formula x = a * r^n, where n is the number of terms in the sequence.
The first step is to determine the first term and the common ratio in the sequence. Then, you can use the formula x = a * r^(n-1) or x = a * r^n to find the value of x in the sequence. Finally, you can check your answer by plugging in the value of x into the original sequence to see if it follows the geometric progression pattern.
Sure, let's say we have a geometric progression with a first term of 3 and a common ratio of 2. If we want to find the value of x in the 5th term, we can use the formula x = 3 * 2^(5-1) = 3 * 2^4 = 48. This means that the 5th term in the sequence is 48.
Yes, there are a few special cases to consider. First, if the common ratio is 1, then the sequence is not geometric and there is no specific value for x. Second, if the common ratio is 0, then all of the terms in the sequence will be 0, making it impossible to find a specific value for x. Lastly, if the common ratio is a negative number, the sequence will alternate between positive and negative values, so you will need to be careful when finding the value of x.