A bag contains 40 red and green marbles. The number of green marbles, g, is 9 times the number of red marbles, r.
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Given:
The sum of two terms of GP is 6 and that of first four terms is
To find:
The sum of first six terms.
Solution:
We have,
Sum of first n terms of a GP is
...(i)
Putting n=2, we get
...(ii)
Putting n=4, we get
(Using (ii))
Divide both sides by 6.
Taking square root on both sides, we get
Case 1: If r is positive, then using (ii) we get
The sum of first 6 terms is
Case 2: If r is negative, then using (ii) we get
The sum of first 6 terms is
Therefore, the sum of the first six terms is 7.875.