Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.

Correct answer:

q =  -5
a₂ =  -2

Step-by-step explanation:

$$\begin{gathered} a_3=10 \\ {a}_1+a_2=-1.6 \\ {a}_1-a_2=2.4 \\ {a}_1=(-1.6+2.4)\mathrm{/}2={\displaystyle \frac{2}{5}}=0.4 \\ {a}_2=-1.6-a_1=-1.6-0.4=-2 \\ {a}_2=q{a}_1 \\ q=a_2\mathrm{/}{a}_1=(-2)\mathrm{/}0.4=-5 \end{gathered}$$

$a_2=(-2)=-2$

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