Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 3, 12, 48, ... Write your answer using decimals and integers. an = _____(_____)n - 1

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Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.   3, 12, 48, ...  Write your answer using decimals and integers.  an = _____(_____)n - 1

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Identify type of sequence: Identify the type of sequence. We have the sequence: 3, 12, 48, ... To determine if the sequence is arithmetic or geometric, we look at the relationship between consecutive terms. 3 to 12 is a multiplication by 4, and 12 to 48 is also a multiplication by 4. Since each term is multiplied by a common ratio to get the next term, the sequence is geometric.Determine first term and ratio: Determine the first term (a1) and the common ratio (r). The first term of the sequence is a1 = 3. To find the common ratio, we divide the second term by the first term: r = 12 / 3 = 4.Write formula for nth term: Write the formula for the nth term of a geometric sequence. The nth term of a geometric sequence is given by the formula an = a1 * r^(n - 1).Substitute values into formula: Substitute the values of a1 and r into the formula. We have a1 = 3 and r = 4. Substituting these values into the formula gives us an = 3 * 4^(n - 1).

Write an equation to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $3,\,12,\,48,\,\ldots$ $\newline$ Write your answer using decimals and integers. $\newline$ $a_n =$ $\_\_\_\_$ $\left(\_\_\_\_\right)^{n - 1}$

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