What is the fifth term of a sequence whose first term is 5 and whose common ratio is 3 ? 1,215 405 243

To find the fifth term of a geometric sequence, you can use the formula for the nth term: \( a_n = a_1 \times r^{(n-1)} \), where \( a_1 \) is the first term, \( r \) is the common ratio, and \( n \) is the term number. In this case, \( a_1 = 5 \), \( r = 3 \), and \( n = 5 \). Plugging in the values gives us: \( a_5 = 5 \times 3^{(5-1)} = 5 \times 3^4 = 5 \times 81 = 405 \). So, the fifth term is 405! Another way to think of this is to visualize the sequence as a multiplying game. Each term magnifies the previous term by a factor of 3. Starting with 5, we move to 15, then 45, then 135, and finally arrive at a towering 405! Keep this technique in mind for your future geometric sequences – they grow quickly!