一个等差数列的首项为 5，公差为 6。

对于该数列，求所有介于 150 和 400 之间的项的和。

先用通项找出符合区间的项号。用截至末项的和减去所选区间之前的和。

The $n$th term is $5+6(n-1)=6n-1$. The inequality $150<6n-1<400$ gives $151/6<n<401/6$. Thus the selected terms have indices $26$ through $66$. Since

their sum is $S_{66}-S_{25}=13200-1925=11275$.

也可把区间内的项看成一个新的等差数列。找出首末项后，用它们的平均数乘项数。

The terms are all of the form $6n-1$. The first above $150$ is $155$ and the last below $400$ is $395$. This gives $(395-155)/6+1=41$ terms. Their sum is