The sum of the first two terms and the sum to infinity of a geometry progression are 48/7 and 7 respectively. Find the values of the common ratio r and the first term when r is positive.
Accepted Solution
A:
Answer:r = ±1/√7a₁ = 7 − √7Step-by-step explanation:The first term is a₁ and the second term is a₁ r.a₁ + a₁ r = 48/7The sum of an infinite geometric series is S = a₁ / (1 − r)a₁ / (1 − r) = 7Start by solving for a₁ in either equation.a₁ = 7 (1 − r)Substitute into the other equation:7 (1 − r) + 7 (1 − r) r = 48/71 − r + (1 − r) r = 48/491 − r + r − r² = 48/491 − r² = 48/49r² = 1/49r = ±1/√7When r is positive, the first term is:a₁ = 7 (1 − r)a₁ = 7 (1 − 1/√7)a₁ = 7 − 7/√7a₁ = 7 − √7