Question

Find S20 for the geometric series 4 + 12 + 36 + 108 + …

5,034,043,187

5,123,498,245`

6,973,568,800

7,321,089,348

Answer 1

for geometric series
\[S_n = a_1 \times (\frac{ 1 - r^n }{ 1 - r } )\]

Answer 2

so what does that mean

Answer 3

a_1 is first term i.e 4
r is common ratio i.e 3

Answer 4

so for S_20
\[S_{20} = 4 \times \frac{ 1 - 3^{20} }{ 1 - 3 } \]

Answer 5

Find the common ratio, r, by dividing a term by its previous term.
Then substitute 4 for a1, the value you find for r for r, and 20 for n in the formula @rishavraj gave you above.

Answer 6

thank you!!