Question

Find an equation for the nth term of the arithmetic sequence.

a19 = -58, a21 = -164 (2 points)


an = 896 - 53(n - 2)
an = 896 - 53(n - 1)
an = 896 + 53(n + 1)
an = 896 - 53(n + 1)

Answer 1

an = 896 - 53(n - 1)

`a _(19) = l + (19 - 1) * d \\ - 58= l+ 18d - - - (i) \\ \\ a _(21) = l + (21 - 1)d \\ - 164 = l + 20d - - - (ii) \\ (ii) - (i) : \: - 106 = 2d \\ d = - 53 \\ hence : l = - 58 - (18 * - 53) \\ l = 896 \\ = > a _(n) = 896 + (n - 1) * - 53 \\ a _(n) = 896 - 53 (n - 1)`