Instructions: Identify the type of sequence and write the explicit rule. Sequence: 3,−6,12,−24,…3,−6,12,−24,…Type: Answer 1 Question 6Explicit Rule: an=𝑎𝑛= Answer 2 Question 6 (( Answer 3 Question 6 )n−1
Question
Instructions: Identify the type of sequence and write the explicit rule. Sequence: 3,−6,12,−24,…3,−6,12,−24,…Type: Answer 1 Question 6Explicit Rule: an=𝑎𝑛= Answer 2 Question 6 (( Answer 3 Question 6 )n−1
Solution
The given sequence is: 3, -6, 12, -24,...
Step 1: Identify the type of sequence This sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio.
Step 2: Write the explicit rule In this sequence, each term is -2 times the previous term. Therefore, the common ratio (r) is -2.
The explicit rule for a geometric sequence is given by: an = a1 * r^(n-1)
Where: an is the nth term a1 is the first term r is the common ratio n is the term number
So, for this sequence, the explicit rule would be: an = 3 * (-2)^(n-1)
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