Question

Raj plants a jasmine on his 7th Birthday.If the plant has one Jasmine to start with,and number of jasmines triples every week,then how many jasmines will there be after x number of weeks

Answer 1

Raj plants a jasmine on his 7th birthday and the plant has 1 jasmine to start with.
Then, 1st week there is 1 jasmine;
         2nd week there is 3 jasmine; (as no. of jasmine triples every week)
          3rd week there is 9 jasmine;
           4th week there is 27 jasmine and so on which forms a G.P. series with first term a₁=1, common ratio r=3.
Then, the number of jasmine after x number of weeks will be
S= a₁ {(rˣ-1)/(r-1)}
   =1×{(3ˣ-1)/(3-1)}
   =(3ˣ-1)/2