The sum of the first $n$ terms of a sequence is given by $S_n=\dfrac{3n^2}{2}-2n$. Express \(u_n

Question

The sum of the first $n$ terms of a sequence is given by $S_n=\dfrac{3n^2}{2}-2n$. Express $u_n$, the nth term of the sequence, in terms of $n$. Show that the sequence is arithmetic. It is given that $$\sum_{r=n+1}^{2n}u_r=300+\sum_{r=1}^{n}u_r$$ Find the value of $n$.

Accepted Answer

$u_n=3n-\frac72$; common difference $3$; $n=10$.

Solution:

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