1Question 1
Find the sum of the geometric series: $3 + 6 + 12 + 24 + 48$.
2Question 2
Calculate the sum: $\sum_{k=1}^{6} 5(2)^{k-1}$.
3Question 3
Find the sum of the first 8 terms of the geometric sequence with $a = 1$ and $r = 0.5$.
4Question 4
A geometric series has $a = 4$, $r = 3$, and $S_n = 484$. Find the number of terms $n$.
5Question 5
The sum of the first 4 terms of a geometric series is 40, and the first term is 5. Find the common ratio $r$.
6Question 6
Calculate: $\sum_{i=0}^{5} 100(0.8)^i$.
7Question 7
A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 60% of its previous height. Find the total vertical distance traveled by the ball after 5 complete bounces (down and up).
8Question 8
Find $k$ if $\sum_{n=1}^{k} 2^n = 510$.
9Question 9
A company's revenue grows by 15% each year. If their revenue in year 1 is R1,000,000, what is their total revenue over the first 10 years?
10Question 10
The first three terms of a geometric sequence are $x-1$, $x+1$, and $3x-1$. Find $x$ and the sum of the first 6 terms.