Write a possible explicit rule for the nth term.
20, 40, 80, 160, 320
a sub n = 20(2)^n-1?
That seems to work.
You're doubling the number.e.g. 20 +20 =40
Yes, that is correct. The explicit rule for the nth term in the sequence 20, 40, 80, 160, 320 is a sub n = 20(2)^(n-1).
Yes, you are correct. The explicit rule for this sequence is indeed a sub n = 20(2)^(n-1).
To explain how to get this explicit rule, we can analyze the pattern in the sequence. Notice that each term is obtained by multiplying the preceding term by 2. If we express this pattern algebraically, we can say that each term, except for the first term, is equal to twice the previous term.
Let's break it down:
- The first term is 20.
- The second term is obtained by multiplying the first term by 2: 20 * 2 = 40.
- The third term is obtained by multiplying the second term by 2: 40 * 2 = 80.
- The fourth term is obtained by multiplying the third term by 2: 80 * 2 = 160.
- The fifth term is obtained by multiplying the fourth term by 2: 160 * 2 = 320.
So, we can generalize the pattern and say that the nth term, denoted as a sub n, is obtained by multiplying the (n-1)th term by 2. In other words, a sub n = 2 * a sub (n-1).
To simplify this, we can substitute a sub n-1 with a sub n-1 = 20(2)^(n-1-1), which equals 20(2)^(n-2). Thus, the formula becomes a sub n = 2 * 20(2)^(n-2).
Simplifying further, we get a sub n = 20(2)^(n-1).
So, you are correct! The explicit rule for this sequence is a sub n = 20(2)^(n-1).