The second and fifth terms of a geometric progression (GP) are 1 and 1 respectively.find (a) common ratio
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8
I think that the attempt at including a fraction has bungled the posting. I read it as
The second and fifth terms of a geometric progression (GP) are 1 and 1/8 respectively. Find (a) common ratio
T5/T2 = r^3 = 1/8
so,
r = 1/2
Use your definitions
2nd term : ar = 1
5th term : ar^4 = 1
divide:
r^3 = 1
r = 1
the ar = 1
a(1) = 1
a = 1
your GP is 1,1,1,....
(not a very exciting sequence, some authors would exclude r = 1 in a GP)
To find the common ratio of a geometric progression (GP), we need to use the formula:
aₙ = a₁ * r^(n-1)
where aₙ represents the nth term, a₁ represents the first term, r represents the common ratio, and n represents the term number.
Given that the second term (a₂) is 1, and the fifth term (a₅) is also 1, we can use these values to form two equations:
a₂ = a₁ * r^(2-1) = a₁ * r = 1
a₅ = a₁ * r^(5-1) = a₁ * r^4 = 1
Now, we can solve these two equations simultaneously to find the value of the common ratio (r). We divide the second equation by the first equation:
(a₁ * r^4) / (a₁ * r) = 1 / 1
r^3 = 1
Taking the cube root of both sides, we get:
r = 1^(1/3) = 1
Therefore, the common ratio (r) of the geometric progression is 1.