Question

Write the explicit formula for the geometric sequence.

a1 = -5 a2 = 20 a3 = -80
A. an = -5 • (-4)n


B. an = -5(-4)n-1


C. an = -4(-5)n-1


D. an = -5 • (4)n

Answer 1

find the common ratio first using the geometric sequence formula\[a_n = a_1 r^{n-1}\]\[a_2 = a_1r^{2 - 1}\]\[a_2 = a_1 r\]\[r = \frac{a_2}{a_1}\]\[r = \frac{20}{-5} = -4\]then just write the formula again using the common ratio\[a_n = a_1 r^{n-1}\]\[a_n = (-5)(-4)^{n-1}\]