Problema Solution
I left out some pizza last night and I’m paying for my mistake this morning. When I got up I counted
50 ants. I followed their trail back and saw that more were coming. In fact, I noticed a group of 10.
Next came a group of 13. After that, a group of 16 marched in. Each group was bigger than the
previous group by 3 ants. This pattern continued through 13 more groups of ants. All in all, I saw 16
groups of ants march in.
a) How many ants arrived in the last group?
b) How many ants total were present after the last group marched in?
Answer provided by our tutors
1st group is: a1 = 10 ants
2nd group: a2 = 10 + 1*3
3rd group: a3 = a2 + 3 = 10 + 2*3
4th group: a4 = a3 + 3= 10 + 3*3
.......
16th group: a16 = 10 + 15*3
a) The last sixteenth group had: a16 = 10 + 15*3 = 55 ants
b) The total of ants present was:
50 + a1 + a2 + ... + a16 = 50 + 10 + 10 + 1*3 + ...+10 + 15*3 = 50 + 16*10 + 3(1 + 2 + ... + 15) = 210 + 3*15*16*(1/2) = 570 ants