What is the 4th term of the geometric sequence if the common ratio is 3 and the 6th is 36.
Answer (1)
Answer:To find the 4th term of a geometric sequence when the common ratio is 3 and the 6th term is 36, follow these steps:1. **Find the first term (a1):** The formula for the nth term of a geometric sequence is: an = a1 × r^(n - 1) For the 6th term (a6): a6 = a1 × r^(6 - 1) 36 = a1 × 3^5 36 = a1 × 243 a1 = 36 / 243 a1 = 4 / 272. **Find the 4th term (a4):** Using the formula for the nth term: a4 = a1 × r^(4 - 1) a4 = (4 / 27) × 3^3 a4 = (4 / 27) × 27 a4 = 4 × 3 a4 = 12So, the 4th term of the geometric sequence is 12.
