Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).
The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.
Here's how you can use the recursive formula to find the terms of the sequence:
a_1 = 2
a_2 = 3a_1 = 3 * 2 = 6
a_3 = 3a_2 = 3 * 6 = 18
a_4 = 3a_3 = 3 * 18 = 54
a_5 = 3a_4 = 3 * 54 = 162
and so on.
To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:
a_n = 3a_(n-1)
a_n / 3 = a_(n-1)
a_n / 3 = (3a_(n-2)) / 3
a_n / 3 = 3^(n-2)
a_n = 3^n
Therefore, the explicit formula for this sequence is a_n = 3^n.
Explanation: