8-5 Geometric Sequences — Practice Questions

1. 1. What is the 7th term of the geometric sequence 5, 10, 20, 40, ...?

2. 2. The 6th term of a geometric sequence is 160 and the common ratio is 2. What is the first term of the sequence?

   • A. 5
   • B. 8
   • C. 10
   • D. 80

3. 3. In the geometric sequence 4, 12, 36, ..., which term has a value of 324? The term number is ___.

4. 4. A geometric sequence has a first term of 2 and a common ratio of 4. The value of the 5th term is ___.

5. 5. In the geometric sequence 1, 5, 25, 125, ..., which term number corresponds to the value 625?

   • A. 4
   • B. 5
   • C. 6
   • D. 7

6. 6. Write the explicit formula for a geometric sequence with a first term of 7 and a common ratio of 4. Use `n` for the term number. $a_n =$ ___

7. 7. Which is the explicit formula for the geometric sequence $2, 8, 32, \dots$?

   • A. $a_n = 2 \cdot 4^{n-1}$
   • B. $a_n = 4 \cdot 2^{n-1}$
   • C. $a_n = 2 + 4(n-1)$
   • D. $a_n = 2 \cdot 4^n$

8. 8. A geometric sequence begins with the terms $6, -12, 24, \dots$. What is the explicit formula for this sequence? Use `n` for the term number. $a_n =$ ___

9. 9. Which explicit formula describes the geometric sequence $80, 20, 5, \dots$?

   • A. $a_n = 80 \cdot 4^{n-1}$
   • B. $a_n = 80 \cdot (\frac{1}{4})^{n-1}$
   • C. $a_n = \frac{1}{4} \cdot 80^{n-1}$
   • D. $a_n = 80 - 60(n-1)$

10. 10. A geometric sequence has a first term of 10 and a second term of 50. Write the explicit formula for this sequence. $a_n =$ ___