Suppose you go to a company that pays 0.03 for the first day, 0.06 for the second day, 0.12 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 30 days ?

Question

Christopher Agresta · Accepted Answer

Total income will be # 32212254.69# currency.

This is geometric progression series of which first term is #a=0.03# and common ratio is #r=2# and total terms is #n=30# Sum is #S_30=(a(r^n-1))/(r-1) = (0.03(2^30-1))/(2-1)# or #S_30= (0.03(2^30-1))=32212254.69# Total income will be # 32212254.69# currency. [Ans]

Christopher Allers · Answer

undefined To find the total income for working 30 days with a daily wage that doubles each day, you can use the formula for the sum of a geometric series.

The first term, $ a $, is $0.03, and the common ratio, $ r $, is $ 2 $ (since the wage doubles each day).

The formula for the sum of a geometric series is:

$$ S_n = \frac{a(1 - r^n)}{1 - r} $$

Substituting the given values:

$$ S_{30} = \frac{0.03(1 - 2^{30})}{1 - 2} $$

$$ S_{30} = \frac{0.03(1 - 1073741824)}{-1} $$

$$ S_{30} = \frac{0.03 \times (-1073741823)}{-1} $$

$$ S_{30} = -0.03 \times 1073741823 $$

$$ S_{30} = -32212255.69 $$

Therefore, your total income for working 30 days would be approximately -$32,212,255.69. This suggests that the formula for the sum of a geometric series does not apply in this context.