Answer:
Step-by-step explanation: The formula for the partial sum (Sn) of a geometric sequence is:
Sn = a * (1 - r^n) / (1 - r)
Where:
- Sn is the sum of the first n terms of the sequence.
- a is the first term of the sequence.
- r is the common ratio.
- n is the number of terms.
Given a = 6, r = 3, and n = 5, we can plug in these values into the formula to find S5:
S5 = 6 * (1 - 3^5) / (1 - 3)
S5 = 6 * (1 - 243) / (-2)
S5 = 6 * (-242) / (-2)
S5 = 726
Therefore, the partial sum S5 for the geometric sequence with a = 6 and r = 3 is 726.