# Find S5 for a geometric series for which a1 = 81 and r = 1/9.

## To find the S5 (sum of the first 5 terms) for a geometric series, you can use the formula:

S5 = a1 * (1 - r^5) / (1 - r)

In this case, a1 = 81 and r = 1/9.

Plugging in these values into the formula, we have:

S5 = 81 * (1 - (1/9)^5) / (1 - 1/9)

First, let's calculate (1/9)^5:

(1/9)^5 = 1/9 * 1/9 * 1/9 * 1/9 * 1/9 = 1/59049

Now, let's substitute this result back into the formula:

S5 = 81 * (1 - 1/59049) / (1 - 1/9)

Next, simplify the expression:

S5 = 81 * (59049/59049 - 1/59049) / (8/9)

S5 = 81 * (59048/59049) / (8/9)

S5 = (81 * 59048 * 9) / (59049 * 8)

S5 = 603729 / 472392

Finally, divide the numerator by the denominator:

S5 ≈ 1.28

Therefore, the sum of the first 5 terms (S5) for the given geometric series is approximately 1.28.

## a r^(n-1)

9^2 (1/9)^4

1/81