Answer:
Step-by-steThe rule for the geometric sequence 1, 3, 9, 27, ... is that each term is obtained by multiplying the previous term by a constant value. In this sequence, the constant value is 3.
Here's a step-by-step explanation:
1. Start with the first term, which is 1.
2. To get the second term, multiply the first term (1) by the constant value (3). This gives us 3.
3. To get the third term, multiply the second term (3) by the constant value (3) again. This gives us 9.
4. To get the fourth term, multiply the third term (9) by the constant value (3) once more. This gives us 27.
5. This pattern continues, where each term is obtained by multiplying the previous term by 3.
In general, for a geometric sequence, the rule can be expressed as:
term_n = term_(n-1) * r
where term_n represents the nth term, term_(n-1) represents the previous term, and r is the common ratio or constant value.
In the given sequence, the common ratio or constant value is 3, so we have:
term_n = term_(n-1) * 3
This rule can be used to find any term in the sequence by multiplying the previous term by 3.
For example, to find the 5th term, we can use the formula:
term_5 = term_4 * 3
term_5 = 27 * 3
term_5 = 81
Therefore, the 5th term in the sequence is 81.p explanation: