Here are the essential concepts you must grasp in order to answer the question correctly.
Geometric Sequence
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 1, 2, 4, 8, the common ratio is 2, as each term is obtained by multiplying the previous term by 2.
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General Term Formula
The general term (nth term) of a geometric sequence can be expressed using the formula a(n) = a(1) * r^(n-1), where a(1) is the first term, r is the common ratio, and n is the term number. This formula allows us to calculate any term in the sequence based on its position.
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Finding Specific Terms
To find a specific term in a geometric sequence, such as the eighth term (a(8)), you substitute n with 8 in the general term formula. For the sequence 1, 2, 4, 8, using the formula a(n) = 1 * 2^(n-1), we can calculate a(8) = 1 * 2^(8-1) = 128.
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