Final answer:
To find the common ratio (r) in a geometric sequence, we can use the formula for the nth term of a geometric sequence. The common ratio can be found by taking the square root of the ratio of two terms in the sequence. In this case, the common ratio is ±√5.
Step-by-step explanation:
To find the common ratio (r) in a geometric sequence, we can use the formula for the nth term of a geometric sequence, which is given by:
tₙ = t₁ * r^(n-1)
From the given information, we have s₂ = 10 and s₄ = 50. Let's substitute these values into the formula:
s₂ = t₁ * r^(2-1) = t₁ * r
s₄ = t₁ * r^(4-1) = t₁ * r^3
Since we have two equations involving t₁ and r, we can solve for r by taking the ratio of the two equations:
s₄/s₂ = (t₁ * r^3) / (t₁ * r) = r^2
Substituting the given values, we get:
50/10 = r^2
Simplifying the equation, we have:
r^2 = 5
Taking the square root of both sides of the equation, we find that:
r = ±√5