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Question

Find an explicit formula for the arithmetic sequence of 12,5,-2,-9

Solution

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From the given, we have: a1=12a_1=12 (first term) and d=512=7d=5-12=-7 (common difference)

The explicit formula\color{#c34632}{\textbf{explicit formula}} is given by:

an=a1+(n1)d, for n1a_n=a_1+(n-1)d,\text{ for }n\geq 1

Substitute given and simplify:

an=12+(n1)(7)a_n=12+(n-1)(-7)

an=127n+7a_n=12-7n+7

an=7n+19\color{#c34632}{a_n=-7n+19}

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