Geometric Sequences and the Explicit Formula Worksheet with Answer Key

What's on the worksheet

1. Give the first term, common ratio and fourth term for each rule.
   a_n = 5 \cdot 2^{n-1}a_n = -3 \cdot 4^{n-1}a_n = 64\left(\dfrac{1}{4}\right)^{n-1}a_n = 10(-0.5)^{n-1}a_n = \dfrac{1}{3} \cdot 6^{n-1}
2. Decide whether the given number is a term of each sequence, and which term.
3. Word problem: the value of Hannah's car at the end of each year.
4. Explain each student's mistake with the explicit formula and find the correct term.
5. Decide which terms share a sign with the first term when the ratio is negative.
6. Word problem: views of a shared video on day 2 and day 5.
7. Find the ratio and explicit formula when the first two terms add to 15.