Ten more each day

On the first day I could skip ten times before the rope caught my feet. My friend said: add ten more each day, and no more than that.

Day $1$: $s_1=10$ skips. Rule: $10$ more each day, no more.

Skips on day $n$: $s_n$. $s_1=10,s_{n+1}=s_n+10$.

On day two I skipped twenty, on day three thirty, and so on. On day seven I skipped seventy, and it felt almost easy, because the day before I had done sixty.

Day $n$: $s_n=10n$ skips. Day $7$: $10\times 7=70$, and the day before $60$.

$s_n=10n$, so $s_7=70,s_6=60$.

After one week I had skipped two hundred and eighty times in all. After thirty days the total was four thousand six hundred and fifty, although on the last day I skipped only three hundred.

Week: $10+20+\cdots +70=280$. Month: ${\sum }_{n=1}^{30}10n=10\times 465=4650$, but the last day only $300$.

${\sum }_{n=1}^{7}10n=280$, ${\sum }_{n=1}^{30}10n=4650$, $s_{30}=300$.

The lesson: a small step every day takes you far. Today's step is only ten more than yesterday's, but the steps pile up. The whole month came to fifteen and a half times the last day.

Each step is only $10$ more than the last: $s_{n+1}=s_n+10$. Yet the steps add up: $4650÷300=15.5$ times the last day.

$4650÷300=15.5$.