The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth ( necessary). 1, 5/2, 25/4 Find the 6th term

1 answer

The nth term of the sequence is given by the formula: \(a_n = a_1 \cdot r^{(n-1)}\) where \(a_1\) is the first term of the sequence, \(r\) is the common ratio, and \(n\) is the term number.

Given the first three terms: 1, 5/2, 25/4

We can find the common ratio by dividing the second term by the first term:
\(r = \frac{5/2}{1} = \frac{5}{2}\)

The formula for the nth term now becomes:
\(a_n = 1 \cdot (\frac{5}{2})^{(n-1)}\)

To find the 6th term, substitute n = 6 into the formula:
\(a_6 = 1 \cdot (\frac{5}{2})^{(6-1)} = 1 \cdot (\frac{5}{2})^{5} = \frac{3125}{32} \approx 97.656\)

Therefore, the 6th term of the sequence is approximately 97.656.