Medium Practice — Set 1

Quick Recap — AP Sums & Means

• $S_n=\tfrac n2\big(2a+(n-1)d\big)$; nth term from sums: $a_n=S_n-S_{n-1}$.
• Inserting $k$ AMs between $a$ and $b$: common difference $d=\dfrac{b-a}{k+1}$.
• $\sum n=\tfrac{n(n+1)}{2}$, sum of first $n$ evens $=n(n+1)$.
• Three numbers in AP: take them $a-d,\,a,\,a+d$.