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Geometric Sequence Rule

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Geometric sequence rule

A geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by the same constant ratio. The key idea is to identify that common ratio and use it consistently.

1) Find the pattern

Look at two consecutive terms and ask: what number is being multiplied each time? If the ratio is not obvious, compare several pairs of terms to confirm it stays the same.

2) Use the rule

Once the common ratio is known, build the next term by multiplying by that ratio again and again. For a missing term, move step by step from a known term until you reach the target position.

3) Simplify the result

Write the final answer in simplest form. That may mean reducing fractions, simplifying radicals, or combining powers if the expression contains them.

4) Check your work

Substitute your result back into the pattern of the sequence. If each term still comes from multiplying by the same ratio, your answer is consistent.

Useful tip

Be careful not to confuse a geometric sequence with an arithmetic one: geometric sequences change by multiplication, not by adding the same amount.

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