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. |
\[\therefore \] \[{{T}_{n}}=a{{r}^{(n-1)}}\] |
\[\Rightarrow \]\[0.00256=8\times {{\left( \frac{1}{5} \right)}^{n-1}}\] |
\[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}=0.00032\] |
\[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}=\frac{32}{100000}\]\[\Rightarrow \]\[{{\left( \frac{1}{5} \right)}^{n-1}}={{\left( \frac{1}{5} \right)}^{5}}\] |
\[\therefore \]\[n-1=5\]\[\Rightarrow \]\[n=6\] |
You need to login to perform this action.
You will be redirected in
3 sec