Answer:
r = ±1/√7
a₁ = 7 − √7
Step-by-step explanation:
The first term is a₁ and the second term is a₁ r.
a₁ + a₁ r = 48/7
The sum of an infinite geometric series is S = a₁ / (1 − r)
a₁ / (1 − r) = 7
Start by solving for a₁ in either equation.
a₁ = 7 (1 − r)
Substitute into the other equation:
7 (1 − r) + 7 (1 − r) r = 48/7
1 − r + (1 − r) r = 48/49
1 − r + r − r² = 48/49
1 − r² = 48/49
r² = 1/49
r = ±1/√7
When r is positive, the first term is:
a₁ = 7 (1 − r)
a₁ = 7 (1 − 1/√7)
a₁ = 7 − 7/√7
a₁ = 7 − √7
