Carlos who weights 104kg plans to lose 8kg during the first 3months of a diet,6kg during the next 3months,4.5kg during the following 3months and so on. this pattern of weight loss forms a geometric sequence. find the persons weight after a large number of years, assuming their diet is a successfu?
Weight = 104 kg.
a0 = 8 kg : weight loss in 1st quarter
a1 = 6 kg: “ “ “ 2nd “
a2 = 4.5kg: “ “ “ 3rd “
By observation, the common ratio, r = ¾
i.e. a_(n+1) = a_n * r, or a_n = a_0*r^n
For a geometric sequence, the sum to infinity is
S = a0/(1 – r), where a0 = 8 and r = ¾
Then, S = 8 / (1 – ¾) = 8 / (1/4) = 32
Therefore total weight loss over a large number of years is 32 kg.
Weight after this time would be 104 – 32 = 72 kg