To find the equation that describes the given sequence \(7, 14, 28, ...\), we first need to identify the pattern or rule governing the sequence.
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Identify the pattern:
- The sequence starts at 7.
- The second term is \(14\) which is \(7 \times 2\).
- The third term \(28\) is \(7 \times 4\), which can also be expressed as \(7 \times 2^2\).
Observing the values, we notice that each term can be expressed as:
- 1st term: \(7 \times 1 = 7\)
- 2nd term: \(7 \times 2 = 14\)
- 3rd term: \(7 \times 4 = 28\)
The multipliers \(1, 2, 4\) are \(2^{(n-1)}\) for \(n = 1, 2, 3\).
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Write the equation: The nth term of the sequence can be expressed as: \[ a_n = 7 \times 2^{(n-1)} \]
Thus, the final equation describing the sequence is: \[ a_n = 7 \times 2^{(n-1)} \]
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