| Which term of the series \[8+1.6+32+...\] is\[0.00256\]? |
A) 5
B) 7
C) 9
D) 6
Correct Answer: D
Solution :
| \[a=8\]\[\Rightarrow \]\[r=\frac{1.6}{8}=\frac{1}{5}\] |
| Let 0.00256 be the nth term. |
| \[\therefore \] \[{{T}_{n}}=a{{r}^{(n-1)}}\] |
| \[\Rightarrow \]\[0.00256=8\times {{\left( \frac{1}{5} \right)}^{n-1}}\] |
| \[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}=0.00032\] |
| \[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}=\frac{32}{100000}\]\[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}={{\left( \frac{1}{5} \right)}^{5}}\] |
| \[\therefore \]\[n-1=5\]\[\Rightarrow \]\[n=6\] |
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