Given: The second and third terms of a geometric series are 128 and 96 respectively.
Required: The first term.
Explanation:
Let the first term of the Geometric Series is 'a' and common ration is 'r'.
Given that second term is 128 and third term is 96.
So
[tex]\begin{gathered} ar=128 \\ ar^2=96 \end{gathered}[/tex]Dividing both, we get
[tex]\begin{gathered} \frac{ar}{ar^2}=\frac{128}{96} \\ r=\frac{3}{4} \end{gathered}[/tex]Put this in 1st
[tex]\begin{gathered} a(\frac{3}{4})=128 \\ a=\frac{128\times4}{3} \end{gathered}[/tex]Thus
[tex]a=\frac{512}{3}=170.67[/tex]Hence, first term is 170.67
Final Anwer: Option 1 is correct answer.
