Hermina Ferry
Feb 13, 2025
What is the next term in the geometric sequence 16, -4, 1, -1/4?
What is the next term in the geometric sequence 16, -4, 1, -1/4? I would appreciate a detailed breakdown of how to solve this problem, including an explanation of the steps involved.
2 Answers
Feb 13, 2025
I am not good at math, but I am using common sense here. The first term is 16, and the second term is -4. We obtain -4 from the first term by multiplying 16 by -1/4: 16 x -1/4 = -4.
The third term is 1. Let's see if we can derive it by multiplying the second term by -1/4: (-4 x -1/4 = 1).
The same applies to the fourth term; we multiply the third term by -1/4: (1 x -1/4 = -1/4).
Thus, any term can be found by multiplying the previous term by -1/4.
The fifth term will be -1/4 x -1/4 = 1/16.
Now, I am sure a formula can be derived from this, which allows you to find a term without knowing the previous term; you simply input the term number you wish to find, and the formula will provide the term.
I am somewhat mathematically challenged and do not know how to calculate the formula, so I used Google and found this formula that you can use:
An = A1 (r^(n-1)) {Here, n-1 is the exponent of r; check the image for a better understanding}.
n = The term number you want to find.
An = The term you want to find.
r = The common ratio, which in this case is -1/4.
A1 = The first term.
With this formula, knowing the first term (A1) and the common ratio (r), you can find any term you desire.
For example, if we want to find the sixth term:
A6 = 16 [-1/4^(6-1)] = -1/64.
I hope this helps.... Show More
Feb 13, 2025
Since the given sequence is geometric, the ratio of its two consecutive terms will be constant, known as the common ratio. The ratio of -4 to 16 can be simplified to -1/4. The ratio of 1 to -4 can also be simplified to -1/4. Hence, the common ratio is -1/4.
The next term in a geometric sequence is obtained by multiplying the common ratio by the previous term. Therefore, the next term is -1/4 * -1/4 = 1/16. The term after this is 1/16 * -1/4 = -1/64.
Thus, the next two terms of the geometric sequence are 1/16 and -1/64.... Show More
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