in a geometric sequence r=3 a2=12 find a10

1. Identify the given information in the problem:
- Common ratio: r = 3
- Second term: a_2 = 12

2. Use the formula for the n-th term of a geometric sequence:
a_n = a_1 \cdot r^{n-1}

3. Find the first term a_1 using the second term:
a_2 = a_1 \cdot r^{1} \Rightarrow 12 = a_1 \cdot 3 \Rightarrow a_1 = \frac{12}{3} = 4

4. Substitute a_1 and r into the formula for the 10th term:
a_{10} = a_1 \cdot r^{9} = 4 \cdot 3^{9}

5. Calculate:
3^9 = 19683

6. Multiply to find a_{10}:
a_{10} = 4 \cdot 19683 = 78732

7. The answer is:
a_{10} = 78732