Question

consider the first four terms of the sequence below -6 + -12 + -48 + -192 what is the 8th term of this sequence

Answer 1

SOLUTION

The correct option is C

We are dealing with a geometric progression(GP)G with:

$\begin{gathered} \text{first term (a)=-3} \\ common\text{ ratio (r) =}\frac{-12}{-3}=4\text{ or }\frac{-48}{-12}=4 \\ \text{ r=4} \end{gathered}$

The formula used to get the nth term of a GP is:

$T_n=ar^{(n-1)}$

For this question n =8 (8th term)

$\begin{gathered} T_8=-3\times4^{8-1} \\ \text{ =-3}\times4^7 \\ \text{ =-3}\times16,384 \\ \text{ =-49,152} \end{gathered}$

Therefore, the correct option is C