Question

Which rule will find the nth term of the arithmetic sequence

Answer 1

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Try to think of this for a while:\[\begin{array}{l|c|r} n & n\text{th term} & n\text{th term rewritten} \\ \hline 1 & a & a + (1-1)d \\ 2 & a+d& a + (2-1)d \\ 3 & a +2d & a + (3-1)d \\ \hline n & \color{#C00}{?}& \color{#c00}{?} \\ \hline \end{array}\]

Answer 2

The key idea really is to notice that the coefficient of \(d\), the common difference, is turning out to be one less than the number of terms.