Calculate 6414

If we add the same number x to the numbers -1,3,15,51, we get the first four members of the geometric sequence. Calculate the number x and the first four members of the geometric sequence.

Correct answer:

x =  3
a₁ =  2
a₂ =  6
a₃ =  18
a₄ =  54

Step-by-step explanation:

$$\begin{gathered} -1,3,15,51 \\ -1+x,3+x,15+x,51+x \\ q(-1+x)=3+x \\ q(3+x)=15+x \\ -q-3q=3-15 \\ q=(15-3)/(1+3)=3 \\ x=(-q-3)/(1-q)=(-3-3)/(1-3)=3 \end{gathered}$$

$a_1=-1+x=-1+3=2$

$a_2=3+x=3+3=6$

$a_3=15+x=15+3=18$

$a_4=51+x=51+3=54$

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