Geometric sequences and series Quiz

1. A geometric series has $a=5$ and $r=2$. Find $S_6$.

• A. $155$
• B. $310$
• C. $315$
• D. $630$

2. For which values of $r$ does a geometric series have a sum to infinity?

• A. $|r|<1$
• B. $r<1$
• C. $r>1$
• D. $|r|>1$

3. Find the sum to infinity of $12-6+3-\cdots$.

• A. $24$
• B. $16$
• C. $12$
• D. $8$

4. Find the least $n$ for which $3\times2^{n-1}>5000$.

• A. $11$
• B. $12$
• C. $13$
• D. $1667$

5. For which values of $x$ does the series $1+3x+9x^2+\cdots$ converge?

• A. $|x|<3$
• B. $|x|<1$
• C. $|x|<\frac13$
• D. $x<\frac13$