Answer:
r=2,n=7
Step-by-step explanation:
The formula for the sum of the nth term of a Geometric Progression is given as:
Sn = a(1-r^n)/(1-r)
Where n = Number of terms
r = Common ratio
From the above question, we are told that:
The sum of the 1st nth term gp is 127.
Hence:
127 = 1(1-r^n)/(1-r)
We are also told that:
The sum of the reciprocal is 127/64
This means the inverse, the formula is given as:
Sn = 1/a(1-r^n)/(1-r)
127/64 = 1(1-1/r^n)/(1-1/r)
= r^(1-n)(1-r^n)/(1-r)
Solving the above, we obtain:
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
