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Answer:
Step-by-step explanation:
The given sequence is defined recursively as follow
[tex]\begin{cases} a_1:=3\\a_k:=a_{k-1}+(k-1) \quad \text{for }k >1\end{cases}[/tex]
Note: This is easy to see by observation.
We will find the next term of the sequence — that is the 8th term. Use the formula for the kth term given above, we get
[tex]\displaystyle a_8=a_7+(8-1)=24+7=31[/tex]
Hence, the next term should be 31.