Saving in January

On the 1st of January, a student puts $10 in a box. On the 2nd, she puts $20 in the box, and so on, putting the same number of 10-dollars notes as the day of the month. How much money will be in the box if she keeps doing this for

a) the first ten days of January
b) the whole of January?

Correct answer:

a =  550
b =  4960

Step-by-step explanation:

$$\begin{gathered} a_1=10 \\ d=10 \\ {n}_1=10 \\ {a}_{10}=a_1+(n_1-1)\cdot d=10+(10-1)\cdot 10=100 \\ a=\frac{a_1+a_{10}}{2}\cdot n_1=\frac{10+100}{2}\cdot 10=550 \end{gathered}$$

$$\begin{gathered} n_2=31 \\ {a}_{31}=a_1+(n_2-1)\cdot d=10+(31-1)\cdot 10=310 \\ b=\frac{a_1+a_{31}}{2}\cdot n_2=\frac{10+310}{2}\cdot 31=4960 \end{gathered}$$

Try another example