Arithmetic Sequences & Series — practice questions

Find the general term and the 30th term of the arithmetic sequence $7, 11, 15, 19, \ldots$

A theatre has 18 seats in the front row, and each row behind has 3 more seats than the one in front. If there are 24 rows, how many seats are in the back row, and which row is the first to have more than 60 seats?

In an arithmetic sequence, the 4th term is $p$ and the 9th term is $q$. Find expressions for $d$ and $a$ in terms of $p$ and $q$, and show that the 14th term is $2q - p$.

Find the sum of the first 25 terms of the arithmetic series $6 + 10 + 14 + \cdots$

How many terms of the arithmetic series $5 + 9 + 13 + \cdots$ are needed for the sum to reach 1230?

The sum of the first $n$ terms of an arithmetic series is given by $S_n = 3n^2 + 5n$. Find the first term, the common difference, and a formula for the $n$th term. Explain the relationship between $S_n$ and $u_n$ that you used.