FractalsGeometric Sequences No need to do questions A or B o

Fractals/Geometric Sequences. No need to do questions A or B on the first page. Please show all work

Solution

Let a_n be the number of branches grown in nth year

From the data we observed that  number of branches grown in nth year is twice to the number of branches grown in n-1 th year

so a_n=2a_n-1

The above sequence forms geometric series with common ratio r=2

given a₀=1

so a_n=a₀r^n-1

a_n=2^n-1

since S_n=a(rⁿ-1)/(r-1)

S₁₀=1(2¹⁰-1)/(2-1) =1023