Answer:
The answer is below
Explanation:
Second term of a geometric series is 2, the limiting sum is 9.
Get the values of first term a and common ratio r.
Solution:
A geometric series is in the form:
a + ar + ar² + ar³ + . . . + arⁿ ⁻ ¹
Where a is the first term, n is the nth term and r is the second ratio.
Since the second term of the series is 2, hence:
ar⁽² ⁻ ¹⁾ = 2
ar = 2 (1)
Also, the limiting sum is 9, hence:
a/ (1 - r) = 9
a = 9 - 9r (2)
Substitute a = 9 - 9r in eqn 1:
(9 - 9r)r = 2
9r - 9r² = 2
9r² - 9r + 2 = 0
9r² - 6r - 3r + 2 = 0
3r(3r - 2) -1(3r - 2) = 0
(3r - 1)(3r - 2) = 0
r = 1/3 or r = 2/3
When r = 1/3; a = 9 - 9r = 9 - 9(1/3) = 6
When r = 2/3; a = 9 - 9r = 9 - 9(2/3) = 3