BARC Quiz 2: Solution and Q&A

Quiz 2 - Part 1

1. The sum of three numbers is 7 and the sum their reciprocals is 7/5. If these three numbers form into a GP, find their product.
2. Find the sum of $1 + 2\left( \dfrac{1}{3} \right) + 3\left( \dfrac{1}{3} \right)^2 + 4\left( \dfrac{1}{3} \right)^3 + \ldots + n\left( \dfrac{1}{3} \right)^{n − 1} + \ldots$
3. A sequence of numbers is defined by the relation $\dfrac{a_{n+1}}{a_n} = 3^n$ and it is known that $a_1 = 1$. Find the value of $\log_3 a_{100}$.

Quiz 2 - Part 2

1. The following three terms are in geometric progression: $x$, $2x + 7$, $10x - 7$. What is the 6^th term?
2. Shureka Washburn has scores 72, 67, 82 and 79 on her algebra tests. Use an inequality to find the scores she must take on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two test.
3. Indirect Mail Inc. had been mailing out coupons for a clearance sale at a constant rate for 4 days, when they counted the coupons, they still had mail out and discovered they had 120,000 left. After 7 total days of work they had 75,000 left. At what rate are they mailing coupons out?
4. Consider the arithmetic sequence whose first term is 3 and common difference is -5. Write an expression for the general term $a_n$. Hint: $a_n = a_1 + (n - 1)d$.

Quiz 2 - Part 3

1. For a known GP, $a_1 = 5/21$ and $r = 1.2$. Calculate the product of the first 21 terms.
2. The sequence $a$, $b$, $c$ is an AP and the sequence $a$, $b$, $c + 1$ is in GP. If $a = 1$, find the value of $c$.
3. How many three-digit numbers are not divisible by 3?