A) 7
B) 8
C) 27
D) 28
E) 31
Correct Answer: A
Solution :
Let number of terms be n. \[\therefore \] \[5461=\frac{1({{4}^{n}}-1)}{4-1}\] \[\Rightarrow \] \[5461\times 3={{4}^{n}}-1\] \[\Rightarrow \] \[{{4}^{n}}=16384\] \[\Rightarrow \] \[{{4}^{n}}={{4}^{7}}\] \[\Rightarrow \] \[n=7\] \[\therefore \]7 terms of GP make the sum 5461.
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