Sequences: แบบฝึกหัด

The first four terms of an arithmetic sequence are 7, 13, 19, and 25.
Work out the 10th term of this sequence.

A sequence is given by 4, 11, 18, 25, ...
Find an expression, in terms of \(n\), for the \(n\)th term of this sequence.

An arithmetic series has a first term of 10 and a common difference of 4.
If the sum of the first \(n\) terms is 960, find the value of \(n\).

The \(n\)th term of a sequence is given by the formula \(u_n = n^2 + 2n\).
Find the value of the 12th term of this sequence.

Three consecutive terms of an arithmetic sequence are \(3x + 2\), \(5x - 1\), and \(6x + 3\).
Find the value of \(x\).

A sequence has an \(n\)th term formula of \(n^2 - 5\). Find the 10th term of this sequence.

In an arithmetic sequence, the 3rd term is \(10\) and the 6th term is \(19\). Find the sum of the first \(8\) terms.

The first term of an arithmetic sequence is 5 and the common difference is 4. The sum of the first \(n\) terms of the sequence is 324. Find the value of \(n\).

The first four terms of an arithmetic sequence are 5, 12, 19, 26.

(a) Write down an expression, in terms of \( n \), for the \( n \)th term of this sequence.

(b) Find the sum of the first 20 terms of this sequence.

An arithmetic sequence has a first term of 14 and a common difference of \(-3\).

(a) Find the 10th term of the sequence.

(b) Find an expression, in terms of \(n\), for the \(n\)th term of this sequence.

(c) The \(k\)th term of the sequence is \(-55\). Find the value of \(k\).