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Answer:
Common ratio = 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
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
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)
Simplifying we have:
1/64 = r^(1-n)
or,
r^(n-1) = 64
r^(n-1) = 2⁶
Hence:
r = 2
Solving for n
n - 1 = 6
n = 6 + 1
n = 7
Therefore:
Common ratio = 2
n = 7