Question

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)

Answer 1

`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 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |* (-1) \\ -164=a_1+20d \\ \\ 58=-a_1-18d \\ \underline{-164=a_1+20d} \\ -106=2d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 2 \\ d=-53`


`-58=a_1+18d \\ -58=a_1+18 * (-53) \\ -58=a_1-954 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |+954 \\ a_1=896 \\ \\ \boxed{a_n=896-53(n-1)}`