osanseviero
In a geometric series,
a2=6
a5=48
Which is the first term, which is the constant and write the progression



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osanseviero
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I know that
\[an=a1*r ^{n1}\]
What goes next?

osanseviero
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6=a1*r^(n1) ?

osanseviero
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6=a1*r^(21), 6=a1*r

Noura11
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As you said :
\[a_n=a_1\times q^{n1}\]
where q is the constant of the serie, so we have :
\[a_2=a_1\times q\\a_5=a_1\times q^4\]
Is that true ?

osanseviero
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Yep

Noura11
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so we get :
\[6=a_1\times q~~~~~~(1)\\48=a_1\times q^4~~~(2)\]
Now, we can divide the equation (2) over (1) , what should we get ?

osanseviero
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8=q^3, q=2!

Noura11
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Good. Now the 1st term can be found easily, can't it ?

osanseviero
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yepp :D

osanseviero
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3 :) thanks

osanseviero
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So an=3*2^n1 ?

Noura11
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Yes, it is ! And you are welcome !