GP members

The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?

Correct answer:

x =  14

Step-by-step explanation:

$$\begin{gathered} a_9=2 \\ {a}_{10}=-1 \\ q=a_{10}\mathrm{/}{a}_9=(-1)\mathrm{/}2=-{\displaystyle \frac{1}{2}}=-0.5 \\ a(n)=a_1{q}^{(}n-1) \\ {a}_8=a_9\mathrm{/}q=2\mathrm{/}(-0.5)=-4 \\ {a}_{11}=q\cdot a_{10}=(-0.5)\cdot (-1)={\displaystyle \frac{1}{2}}=0.5 \\ {a}_{12}=q\cdot a_{11}=(-0.5)\cdot 0.5=-{\displaystyle \frac{1}{4}}=-0.25 \\ {a}_{13}=q\cdot a_{12}=(-0.5)\cdot (-0.25)={\displaystyle \frac{1}{8}}=0.125 \\ {a}_{14}=q\cdot a_{13}=(-0.5)\cdot 0.125=-{\displaystyle \frac{1}{16}}=-0.0625 \\ x=14 \\ x>10?? \end{gathered}$$

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