Mathematics
codydambrosia
16

Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164 an = 896 - 53(n - 2) an = 896 - 53(n - 1) an = 896 + 53(n + 1) an = 896 - 53(n + 1)

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(1) Answers
AnnieMarie14

[latex]a_n=a_1+d(n-1) \\ \\ a_{19}=-58 \\ a_{21}=-164 \\ \\ -58=a_1+d(19-1) \\ -164=a_1+d(21-1) \\ \\ -58=a_1+18d \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-1) \\ -164=a_1+20d \\ \\ 58=-a_1-18d \\ \underline{-164=a_1+20d} \\ -106=2d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 2 \\ d=-53[/latex] [latex]-58=a_1+18d \\ -58=a_1+18 \times (-53) \\ -58=a_1-954 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |+954 \\ a_1=896 \\ \\ \boxed{a_n=896-53(n-1)}[/latex]

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