Question

find the first three partial sums of the series.
6 + 18 + 54 + 162 + 486 + 1458 + …
write your answers as integers or fractions in simplest form.
s₁ =
s₂ =
s₃ =

Explanation:

Step1: Find \( S_1 \)

The first partial sum \( S_1 \) is just the first term of the series. The first term is 6, so \( S_1 = 6 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. So we add the first term (6) and the second term (18): \( S_2 = 6 + 18 = 24 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. We add the first three terms: 6, 18, and 54. So \( S_3 = 6 + 18 + 54 = 78 \).

Answer:

\( S_1 = 6 \)
\( S_2 = 24 \)
\( S_3 = 78 \)