A sequence has a first term of 24 and every other term is one half of the previous term.
Find a recursive formula that defines this sequence.
The answer of this question is:
an=an-1*1/2
Somebody can help me and let me know why is 1/2 on the formula? please please!!!
I am not sure if the formula is the right one!!
r = .5
Just as in your other problem, r in a geometric sequence is the ratio of every term to the one before it. That is the very meaning of a geometric sequence.
In this sequence, the formula is given as an = an-1 * 1/2, where an represents the nth term in the sequence and an-1 represents the (n-1)th term.
To understand why 1/2 is used in the formula, let's break down the problem step-by-step:
1. The first term, a1, is given as 24. This is the base value or starting point of the sequence.
2. The question states that every other term is one-half of the previous term. This means that starting from the second term (a2), each term is obtained by multiplying the previous term by 1/2. More specifically:
- a2 = a1 * 1/2
- a3 = a2 * 1/2
- a4 = a3 * 1/2
- and so on.
Therefore, to find any term after the first term, you multiply the previous term by 1/2. This recurring multiplication by 1/2 reflects the pattern mentioned in the question, where each term is half of the previous term.
Hence, the recursive formula for this sequence is an = an-1 * 1/2.
Feel free to ask if you have any further doubts!