himanshuhpr
If we use g.p in this question . And if we consider a=4000 ; r=2 then 4000*2^(n-1) > 250000 --------> 2^n > 125 <------> n=7 . Hence answer is 14 .... Pl. help me find anomaly to above mentioned description...
The confusion comes from the interpretation of the formula:
\(a_1\) is the first term and then \(a_n=a_1R^{n-1}\), which is the term on the \(n\)th place. Between the first term and the \(n\)th term, \(n-1\) multiplications by the ratio \(R\) take place, and this is reflected in the exponent of \(n-1\).
Using the formula, you deduced that if \(a_1=4000\) is the first term, then the 7th term will be greater than 250,000. Between the first population and the 7th one, 6 cycles of 2 hours passed, a total of 12 hours, which is the correct answer.
According to the question, your answer should be \(n-1\) from your formula and not \(n\).
In other posts, \(2^n\) was considered, which means \(n\) represents the number of multiplications by \(n\), and obviously the \((n+1)\)th term is greater than 250,000. In both cases we talk about 6 and 7, the difference is whether you called 6 \(n\) or \(n-1\).