Arithmetic Sequences practice questions — GCSE Maths

In the arithmetic progression $(a_n{)}_{n\ge 1}$, $a_2=7$ and $a_5=16$. Determine $a_1$.

The numbers $5,8,11,14,\dots$ form an arithmetic progression. The common difference $r$ equals:

In an arithmetic progression with $a_1=3$ and $r=4$, the term $a_n=47$. Determine $n$.

Compute the sum of the first $20$ terms of the arithmetic progression $(a_n{)}_{n\ge 1}$ with $a_1=2$ and $r=3$.

In an arithmetic progression, $a_3=11$ and $a_7=27$. Determine $a_5$.

A student deposits $\mathrm{\$}50$ in January and increases the deposit by $\mathrm{\$}10$ every following month. How much will be deposited in total over $12$ months?

The numbers $x-2$, $5$, $x+4$ are in arithmetic progression (in this order). Determine $x$.

For the arithmetic progression with $a_1=1$ and $r=2$, compute $a_5+a_6+a_7+a_8+a_9$.

For an arithmetic progression with $a_1=5$ and $r=3$, find the smallest $n$ such that $S_n\ge 500$.

Three numbers in arithmetic progression have sum $15$ and the sum of their squares is $83$. The largest of them is: