What is the recursive formula for this geometric sequence: 9, 36, 144
Answers
Step-by-step explanation:
Well if you divide 9 by 36 you get 4. Then 144 by 36 you get 4. Therefore the rule is that you multiply the number by 4. 9x4=36 36x4=144 144x4=576 576x4=2,304.
Answer: The recursive formula for a geometric sequence can be derived from its definition. A geometric sequence consists of terms that are formed by multiplying the previous term by a constant, called the common ratio. The formula for the nth term of a geometric sequence is:
an = ar^(n-1)
where a is the first term and r is the common ratio.
To find the recursive formula for the given sequence, we first need to identify the first term and the common ratio.
In this case, the first term is 9 and the common ratio is 3. Therefore, the recursive formula is:
an = 9 * 3^(n-1)
This recursive formula can be used to find any term in the given geometric sequence.
For example, to find the 10th term, we can substitute 10 for n in the recursive formula and get the result:
a10 = 9 * 3^(10-1)
= 9 * 3^9
= 9 * 19,683
a10 = 177,147
Learn more about geometric sequences here
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Learn more about recursive formulas here
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