To find the 5th term of a geometric sequence, we need to know the first term and the common ratio. There are different ways to find the 5th term, including using the definition of a geometric sequence or the general term formula. Here are the steps to find the 5th term of a geometric sequence whose first term is 4 and whose common ratio is -2, as shown in:
- Using the definition of a geometric sequence:
- The first term is a_1 = 4.
- The common ratio is r = -2.
- The 5th term is a_5 = a_1 * r^(5-1) = 4 * (-2)^(4) = 64.
- Using the general term formula:
- The general term formula for a geometric sequence is a_n = a_1 * r^(n-1).
- Substituting a_1 = 4, r = -2, and n = 5, we get a_5 = 4 * (-2)^(5-1) = 64.
Therefore, the 5th term of the geometric sequence with first term 4 and common ratio -2 is 64.
