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9 Partial sums of geometric series \( 9 J \mathrm{~J} \)
Find the \( 9^{\text {th }} \) partial sum of the geometric sequence \( a_{n}=3^{n-1} \).
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Answer

Substitute the values: \(S_9 = \frac{(3^0) (1-3^9)}{1-3}\)

Steps

Step 1 ：Find the common ratio for the geometric sequence: r = 3

Step 2 ：Apply the formula for the sum of a geometric series: S_n = \(\frac{a_1 (1-r^n)}{1-r}\)

Step 3 ：Substitute the values: \(S_9 = \frac{(3^0) (1-3^9)}{1-3}\)