Arithmetic sequences

Positive numbers which when divided by $3$ leave a remainder of $2$ are terms of an increasing arithmetic sequence. The sum of the first $15$ terms is $480$. Find the $3$rd term of this sequence.

The second term of an arithmetic sequence is $-21$, the fifth term is $21$. How many of the first consecutive terms do we have to add up to get a sum of more than $50$?

Find the first term of an arithmetic sequence \( \left\{a_n\right\}_{n=1}^{\infty} \), if the sum of the first eight terms is $12$ and the sum of the first twelve terms is $-6$: \[ \begin{aligned} s_8&=12 \\ s_{12}&=-6 \end{aligned} \]