Question

Identify the 16th term of a geometric sequence where a1 = 4 and a8 = −8,748.

−172,186,884

−57,395,628

57,395,628

172,186,884

Answer 1

first find the common ratio r

a8 / a1 = r^7 = -8748 / 4

Answer 2

16th term = a1 * r^15

Answer 3

\[a_n=a_1*r^{n-1}\]\[a_8=a_1*r^{8-1}\]\[r^7=\frac{a_8}{a^1}\]\[r=\sqrt[7]{\frac{a_8}{a_1}}\]\[r=-3\]\[a_n=a_1*(-3)^{n-1}\]\[a_{16}=a_1*(-3)^{16-1}\]\[a_{16}=a_1*(-3)^{15}\]\[a_{16}=4*(-3)^{15}\]\[\boxed{a_{16}=-57,395,628}\]

Answer 4

thank you both