Beth bought an 8.5-pound bag of cat food. She also bought a bag of dog food that weighs 3.5 times as much as the bag of cat food
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Answer:
Step-by-step explanation:
So we have the sequence:
3, 9, 27...
First, note that this is a geometric sequence because each subsequent term <em>not </em>increasing linearly.
To find the 18th term, we can write an explicit formula.
The standard explicit formula for a geometric sequence is:
Where a is the initial term, r is the common ratio, and n is the nth term.
From the sequence, we can see that the initial term a is 3. The common ratio is 3 since each subsequent term is 3 times the previous term. So, substitute:
To find the 18th term, substitute 18 for n. So:
Subtract:
Evaluate:
Multiply:
And we're done!