Sequences：練習題

Find the next term in the arithmetic sequence: \( 5, 8, 11, 14, \dots \)

Find the \(n\)th term expression for the following linear sequence:
\(11, 8, 5, 2, \dots\)

Generate the first four terms of a sequence given by the position-to-term rule:
Term = \(2n^2 - 3\)

The first four terms of a quadratic sequence are \(4, 9, 16, 25\). Which of the following is an expression for the \(n\)th term of this sequence?

A sequence has the position-to-term rule \(3n + 2\). What is the 5th term of this sequence?

Write down the next term in the geometric progression:
\(3, 6, 12, 24, \dots\)

The first two terms of a Fibonacci-type sequence are \(2\) and \(3\), where each subsequent term is found by adding the previous two terms.
Find the 5th term of this sequence.

The \(n\)th term of a sequence is given by \(5 - 2n\).
Work out the 6th term of this sequence.

Write down the next two terms in the sequence of cube numbers:
\(1, 8, 27, 64, \dots\)

Here are the first four terms of a quadratic sequence:
\(2, 7, 14, 23\)

(a) Find the next two terms of the sequence.
(b) Show that the \(n\)th term of the sequence can be written in the form \(n^2 + 2\).
(c) Find the 20th term of this sequence.