Find an explicit formula for the geometric sequence 12,24,48,96 where the first term should be b(1)

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Identify Terms: Identify the first term (b(1)) and the common ratio (r) of the geometric sequence. The first term b(1) is 12. To find the common ratio, divide the second term by the first term: r = 24 / 12 = 2.Calculate Common Ratio: Use the formula for the nth term of a geometric sequence, which is b(n) = b(1) * r^(n-1), where b(n) is the nth term, b(1) is the first term, and r is the common ratio. Substitute the values of b(1) = 12 and r = 2 into the formula to get b(n) = 12 * 2^(n-1).Use nth Term Formula: Check the formula with the given terms of the sequence to ensure it is correct. For n = 1, b(1) = 12 * 2^(1-1) = 12 * 2^0 = 12 * 1 = 12, which matches the first term. For n = 2, b(2) = 12 * 2^(2-1) = 12 * 2^1 = 12 * 2 = 24, which matches the second term. For n = 3, b(3) = 12 * 2^(3-1) = 12 * 2^2 = 12 * 4 = 48, which matches the third term. For n = 4, b(4) = 12 * 2^(4-1) = 12 * 2^3 = 12 * 8 = 96, which matches the fourth term. The formula is verified with the given terms.

Find an explicit formula for the geometric sequence $12, 24, 48, 96$ where the first term should be $b(1)$

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Find an explicit formula for the geometric sequence $12, 24, 48, 96$ where the first term should be $b(1)$