A quadratic sequence begins $3,x,29,51,\dots$ Find the value of $x$.

In the group stage of a volleyball competition, all the teams in the group have to play each other. When there are four teams in a group, six games are needed for each team to play each of the other teams exactly once. Find the number of games needed for each team to play each of the other teams exactly once in a group of $n$ teams.

Find a general formula for the $n^{th}$ term of the following sequence.

$6,10,14,18,22,26,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$42,35,28,21,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$2,5,10,17,26,37,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$3,8,15,24,35,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$2.5,7,11.5,16,20.5,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$-0.5,4,13.5,28,47.5,\dots$

Find a general formula for the $n^{th}$ term of the following sequence.

$9,13,13,9,1,\dots$