Final answer:
To find the tenth term of the geometric sequence 3, 9, 27, 81, 243, ..., identify the common ratio of 3 and use the geometric sequence formula. The tenth term is calculated as 3 × 39, resulting in 19683.
Step-by-step explanation:
The sequence given is 3, 9, 27, 81, 243, ..., which is a geometric sequence where each term is multiplied by 3 to get the next term (a common ratio of 3). To find the tenth term in this sequence, use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio.
The first term a1 is 3, and the common ratio r is also 3. To calculate the tenth term:
- Plug in the values into the formula: a10 = 3 × 3(10-1)
- Calculate the exponent: 39
- Perform the exponentiation: 39 = 19683
Therefore, the tenth term of the sequence is 19683.