Question

Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164

A.) an = 896 - 53(n - 2)
B.) an = 896 - 53(n - 1)
C.) an = 896 + 53(n + 1)
D.) an = 896 - 53(n + 1)

Answer 1

`a_(n)=a_(1) + (n - 1)\cdot{r}\\\\a_(19)=a_(1)+(19-1)\cdot{r}\\\\-58=a_1+18r\\\\a_1=-18r-58\\\\\\a_(21)=a_1+(21-1)\cdot{r}\\\\-164=a_1+20r\\\\a_1=-20r-164\\\\\\-18r - 58 = - 20r-164\\-18r+20r=-164+58\\2r=-106\\r=-53\\\\a_1=-20r-164\\a_1=-20\cdot{(-53)}-164\\a_1=1060-164\\a_1=896\\\\\boxed{a_n=896+(n-1)\cdot{(-53)}}`


B