91Ó°ÊÓ

In a geometric sequence, each term is generated by multiplying the previous term by a constant called the 'common ratio'. To find any term in the sequence, you can use the 'nth term formula'. The formula is given by:
\[ a_n = a_1 \times r^{(n-1)} \]
Where:

• \( a_n \) is the nth term
• \( a_1 \) is the first term
• \( r \) is the common ratio
• \( n \) is the term number

This formula allows you to find the value of any term in the sequence without calculating all the previous terms. For example, if the first term \( a_1 = 64 \) and the common ratio \( r = \frac{1}{4} \), you can find the 5th term by plugging in the values:
\[ a_5 = 64 \times (\frac{1}{4})^{(5-1)} = 64 \times (\frac{1}{256}) = \frac{1}{4} \]
It's a powerful tool to quickly determine any term in a geometric sequence.
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