Geometric Sequences (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Geometric Sequences: core idea

a_n

formula.

Find the next term: $2,6,18,\ldots$ .

Hint: Multiply by the common ratio to move one term. Answer: 54.

1. Find the common ratio of $81,27,9,\ldots$ .
2. Find the $5$ th term of $3,6,12,\ldots$ .
3. Find $a_1$ if $a_4=54$ and $r=3$ .
4. Find $a_6$ if $a_1=1$ and $r=2$ .
5. Find $1+2+4+8+16$ .
6. Find the product $2\cdot4\cdot8$ .
7. Find the ratio if $a_2=10$ and $a_3=50$ .
8. Find $a_3$ if $a_1=16$ and $r=1/2$ .
9. A bacteria count doubles each hour from $5$ . Find the count after $3$ hours.