Problema Solution
the trunk of a certain tree is 75 cm thick. each year it get thicker by 1 cm. how thick is the tree going to be in 50 years?
Answer provided by our tutors
beginning a0 = 75 cm
after 1 year: a1 = a0 + 1
after 2 years: a2 = a1 + 1 = a0 + 2*1
after n years: an = a0 + n*1 = a0 + n
we can prove this by using the method of Mathematical Induction
let the above statement be true for n = k that is ak = a0 +k
for n = k+1 we have
ak+1 = ak + 1 = a0 + k + 1 = a0 + (k+1)
after 50 years that is for n = 50 the result will be
a50 = a0 + 50 = 75 + 50 = 125 cm
after 50 years the three will be 125 cm thick.