Question
ITEM 16
What is the explicit formula of the geometric sequence 3, 6, 12, 24, 48, ...?
Answers
GPT 3.5
The explicit formula for a geometric sequence is given by:
a_n = a_1 * r^(n-1)
Where:
a_n = the nth term of the sequence
a_1 = the first term of the sequence
r = the common ratio
n = the term number
In this case, the first term (a_1) is 3 and the common ratio (r) is 2 since each term is multiplied by 2 to get the next term.
Therefore, the explicit formula for the given geometric sequence is:
a_n = 3 * 2^(n-1)
a_n = a_1 * r^(n-1)
Where:
a_n = the nth term of the sequence
a_1 = the first term of the sequence
r = the common ratio
n = the term number
In this case, the first term (a_1) is 3 and the common ratio (r) is 2 since each term is multiplied by 2 to get the next term.
Therefore, the explicit formula for the given geometric sequence is:
a_n = 3 * 2^(n-1)