Question

I walk 1.1m forward, then 1.1m back. Then I walk 2(1.1)m, then 3(1.1)m. How far did I walk when I stop at 10m and walk back?

Answer 1

I know\[2(1.1+2(1.1)+3(1.1)+4(1.1)+5(1.1)+6(1.1)+7(1.1)+8(1.1)+9(1.1)+0.1)\]I really need the formula, or sum with remainders... or sumthing (sic).

Answer 2

its an arithmetic series, adding 2.2 each time
stop at n=9 , walk 9.9 there and back
\[S = \frac{9}{2}(2.2 + 19.8) = 99\]
then add the final time, walking 10 there and back
99 + 20 = 119

Answer 3

\[S_n = \frac{n(a_1 + a_n)}{2}\]