Question

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

Answer 1

\[\large a_n = a \cdot r^{n-1}\]

Answer 2

You are given 8th term as:

\[\large 4 \cdot r^{8-1} = -8748 \implies r^7 = 2187 \implies r = \sqrt[7]{2187} \implies r = 3 \]

Answer 3

So now find:

\[\large a_{16} = (4) \cdot (3)^{16-1} \implies \color{green}{a_{16} = 4 \cdot 3^{15}}\]

Find this now..

Answer 4

-3

Answer 5

Oh sorry it is -3 there..

Answer 6

\[\large 4 \cdot r^{8-1} = -8748 \implies r^7 = -2187 \implies r = \sqrt[7]{-2187} \implies r = -3\]

Answer 7

\[\large a_{16} = (4) \cdot (-3)^{16-1} \implies \color{green}{a_{16} = 4 \cdot (-3^{15})}\]

Answer 8

\[\huge a_{16} = -57395628\]