If k+1 2k-1 and 3k+1 are three consecutive term of a Go find the value of the common ratio
To find the common ratio, we'll compare the second term to the first term and the third term to the second term.
Given:
First term (a₁) = k+1
Second term (a₂) = 2k-1
Third term (a₃) = 3k+1
The common ratio (r) can be calculated using the formula: r = a₂ / a₁
Substituting the given values:
r = (2k-1) / (k+1)
We need to simplify this equation to find the common ratio.
r = (2k - 1) / (k + 1)
To simplify the expression, we'll multiply both the numerator and denominator by the conjugate of the denominator:
r = (2k - 1) / (k + 1) * (k - 1) / (k - 1)
r = (2k^2 - 2k - k + 1) / (k^2 - 1)
r = (2k^2 - 3k + 1) / (k^2 - 1)
Therefore, the common ratio (r) is (2k^2 - 3k + 1) / (k^2 - 1).