Write the first five terms of the sequence whose nth term is \(a_n = n(n+2)\).
3, 8, 15, 24, 35
Write the first five terms of the sequence whose nth term is \(a_n = \dfrac{n}{n+1}\).
\(\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}, \dfrac{4}{5}, \dfrac{5}{6}\)
Write the first five terms of the sequence whose nth term is \(a_n = 2^n\).
2, 4, 8, 16, 32
Write the first five terms of the sequence whose nth term is \(a_n = \dfrac{2n - 3}{6}\).
-\(\dfrac{1}{6}\), \(\dfrac{1}{6}\), \(\dfrac{1}{2}\), \(\dfrac{5}{6}\), \(\dfrac{7}{6}\)
Write the first five terms of the sequence whose nth term is \(a_n = (-1)^{n-1} 5^{n+1}\).
25, -125, 625, -3125, 15625
Write the first five terms of the sequence whose nth term is \(a_n = n\left(\dfrac{n^2 + 5}{4}\right)\).
\(\dfrac{3}{2}, \dfrac{9}{2}, \dfrac{21}{2}, 21, \dfrac{75}{2}\)
Find the indicated terms of the sequence whose nth term is \(a_n = 4n - 3\): Find \(a_{17}\) and \(a_{24}\).
65, 93
Find the indicated term for the sequence whose nth term is \(a_n = \dfrac{n^2}{2^n}\): Find \(a_7\).
\(\dfrac{49}{128}\)
Find the indicated term of the sequence whose nth term is \(a_n = (-1)^n 1^n 3^n\): Find \(a_9\).
729
Find the indicated term of the sequence whose nth term is \(a_n = \dfrac{n(n - 2)}{n + 3}\): Find \(a_{20}\).
\(\dfrac{360}{23}\)
Write the first five terms of the recursively defined sequence: \(a_1 = 3\), \(a_n = 3a_{n-1} + 2\) for \(n > 1\). Also write the corresponding series.
3, 11, 35, 107, 323
Series: 3 + 11 + 35 + 107 + 323 + ...
Write the first five terms of the sequence defined by \(a_1 = -1\) and \(a_n = \dfrac{a_{n-1}}{n}\) for \(n \geq 2\). Also write the corresponding series.
-1, -\(\dfrac{1}{2}\), -\(\dfrac{1}{6}\), -\(\dfrac{1}{24}\), -\(\dfrac{1}{120}\)
Series: -1 + (-\(\dfrac{1}{2}\)) + (-\(\dfrac{1}{6}\)) + (-\(\dfrac{1}{24}\)) + (-\(\dfrac{1}{120}\)) + ...
Write the first five terms of the sequence defined by \(a_1 = a_2 = 2\) and \(a_n = a_{n-1} - 1\) for \(n > 2\). Also write the corresponding series.
2, 2, 1, 0, -1
Series: 2 + 2 + 1 + 0 + (-1) + ...
The Fibonacci sequence is defined by \(a_1 = a_2 = 1\) and \(a_n = a_{n-1} + a_{n-2}\) for \(n > 2\). Find \(\dfrac{a_{n+1}}{a_n}\) for \(n = 1, 2, 3, 4, 5\).
1, 2, \(\dfrac{3}{2}\), \(\dfrac{5}{3}\), \(\dfrac{8}{5}\)