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 of 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 a given number is a term of a geometric sequence, and which one.
3. Hannah's car value: model its value each year with a geometric rule.
4. Explain each student's mistake with the explicit formula and find the correct term.
5. Use a negative ratio to decide the sign of terms without working them out.
6. Video views: find the ratio and model the daily views.
7. Find the ratio from the first two terms adding to 15 and write the formula.