Sequences：練習問題

What is the next term in the sequence: 7, 11, 15, 19, ...?

A sequence is defined by the position-to-term rule \( u_n = \frac{3n - 1}{2} \). Calculate the 15th term of this sequence.

The \( n \)th term of a sequence is given by the expression \( an^2 + bn + 4 \). Given that the first term is \( 7 \) and the second term is \( 14 \), find the value of the 3rd term.

A sequence is given by: 5, 8, 11, 14, ...
Find the expression for the \(n\)th term of this sequence.

Deduce the expression for the \(n\)th term of the quadratic sequence: 4, 7, 12, 19, 28, ...

A sequence of numbers follows the term-to-term rule: subtract 6.
If the first term of the sequence is 14, work out the 4th term.

Find an expression, in terms of \(n\), for the \(n\)th term of the linear sequence: \(11, 17, 23, 29, \dots\)

Determine an expression for the \(n\)th term of the quadratic sequence:
2, 9, 20, 35, 54, ...

A sequence is generated using the term-to-term rule: multiply by 3 and subtract 4.
a) If the first term is \(6\), calculate the second and third terms of the sequence.
b) Work out the first term of the sequence if the second term is \(26\).

A linear sequence is given by: 12, 19, 26, 33, ...

(a) Write down an expression for the \(n\)th term of this sequence.
(b) Find the \(40\)th term of the sequence.
(c) Is \(200\) a term in this sequence? You must show your working to justify your answer.