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Bernardo and Ogechi were asked to find an explicit formula for the sequence $1, 8, 64, 512$ where the first term should be $h(1)$

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Find properties of a parabola from equations in general form

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Q. Bernardo and Ogechi were asked to find an explicit formula for the sequence

1, 8, 64, 512

where the first term should be

h(1)

Observe Sequence Pattern: We need to observe the pattern of the sequence to find the explicit formula. The sequence is $1, 8, 64, 512$ . Let's look at the ratio of each term to its previous term to determine if it's a geometric sequence.
Calculate Ratios: Calculate the ratio between the second term and the first term: $8 / 1 = 8$ . Calculate the ratio between the third term and the second term: $64 / 8 = 8$ . Calculate the ratio between the fourth term and the third term: $512 / 64 = 8$ . Since the ratio is constant, it is a geometric sequence with a common ratio of $8$ .
General Form of nth Term: The general form of the $n$ th term for a geometric sequence is given by $h(n) = a \cdot r^{(n-1)}$ , where $a$ is the first term and $r$ is the common ratio. For this sequence, $a = 1$ and $r = 8$ .
Substitute Values: Substitute the values of $a$ and $r$ into the formula to get the explicit formula for the sequence: $h(n) = 1 \times 8^{(n-1)}$ .
Simplify Formula: Simplify the formula to get the final explicit formula: $h(n) = 8^{(n-1)}$ .

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