Question: Find the indicated term of the geometric sequence. 5th term of $1, -3, 9, …$

Find the indicated term of the geometric sequence.

5th term of $1, -3, 9, …$

Solution

To find the 5th term of the geometric sequence \(1, -3, 9, \ldots\), follow these steps: Identify the first term \(a\) and the common ratio \(r\). - The first term \(a = 1\). - The common ratio \(r\) can be found by dividing the second term by the first term, \(r = \frac{-3}{1} = -3\). Use the formula for the \(n\)-th term of a geometric sequence: \[ a_n = a \cdot r^{n-1} \] Substitute \(a = 1\), \(r = -3\), and \(n = 5\) into the formula: \[ a_5 = 1 \cdot (-3)^{5-1} \] Calculate \((-3)^4\): \[ (-3)^4 = 81 \] Therefore, the 5th term \(a_5\) is: \[ a_5 = 1 \cdot 81 = 81 \] The 5th term of the sequence is 81.