Average & Number Series

Level 2

Quest: - Average work done in 1 Day (1st) = 1 unit. Average work done in 2 Days (1st & 2nd) = 1 unit. Average work done in 3 Days (1st, 2nd & 3rd) = 4/3 units. Average work done in 4 Days (1st, 2nd, 3rd & 4th) = 7/4 units. Based on above pattern, find the average work done in 10 Days (1st, 2nd… 9th & 10th Day)?


The answer is 14.3.

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1 solution

Vilakshan Gupta
Mar 14, 2018

The general formula for the average work done can be calculated using the formula i = 1 n F i i \displaystyle \sum_{i=1}^n \frac{F_i}{i} , where F n F_n denotes the n n th Fibbonacci number.

So, average work done in 10 10 days is i = 1 10 F 10 10 = 1 + 1 + 2 + + 55 10 = 143 10 = 14.3 \displaystyle \sum_{i=1}^{10} \frac{F_{10}}{10}=\dfrac{1+1+2+\cdots+55}{10}=\dfrac{143}{10}=\boxed{14.3}

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