The sum of the 1st nth term gp is 127.the sum of the reciprocal is 127/64,if the 1st term is 1.find n and the common ratio

Ratio (r) = 2

n = 7

Step-by-step explanation:

The formula for the sum of the nth term of a G.P is given as:

Sn = a(1-r^n)/(1-r)

Where n = Number of terms

r = Common ratio

The sum of the 1st nth term gp is 127.

Hence:

127 = 1(1-r^n)/(1-r)

The sum of the reciprocal is 127/64

The formula is inverted , hence:

Sn = 1/a(1-r^n)/(1-r)

127/64 = r^(1-n)(1-r^n)/(1-r)

Hence:

1/64 = r^(1-n)

r^(n-1) = 64

r^(n-1) = 2⁶

Hence:

r = 2

Solving for n

n - 1 = 6

n = 6 + 1

n = 7

Therefore:

r = 2

n = 7

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: