Pattern problem

Question

Rita loves eating vegetables. On August 1st, he ate 1 vegetable. On August 2nd he ate 2 vegetables. And so on, until August 18th. How many vegetables did she eat?

Answer 1

According to the information you have provided, it seems that Rita is matching her daily vegetable intake with the August 1st - 18th calendar dates (e.g., eating 1 vegetable on the 1st, 2 on the 2nd, and so on until the 18th). To find out how many vegetables she ate from August 1st-August 18th, we can use an arithmetic series summation formula.

Here is our summation formula: S = #tot/2 * (#start + #finish)

'S' represents our the vegetable sum (the final answer), '#tot' stands for total days, '#start' stands for our first day, and '#finish' stands for our final day.

In total, we have 18 days to consider (we start with August 1st and end with August 18th).

After putting these values into the above formula, we get:

S = 18/2 * (1 + 18)

S = 9 * 19

S = 171

In short, this shows that 1+2+3+...+18 = 171.

Therefore, from August 1st to August 18th, Rita ate a total of 171 vegetables. Yum!

Answer 2

1+2+3+... +16+17+18

is an arithmetic sequence

a1,a2...an has a sum of n/2 times (1st + last) = 18/2(a1+an) = 9(1+18)=9(19) = 171

or use Gaus' formual n(n+1)/2 = 18(18+1)/2 = 9(19) = 171

1st 3 numbers sum to 6

last 3 sum to 51

2nd 3 sum to 4+5+6= 15

2nd to last 3 sum to 15+14+13 = 42

3rd sum to 7+8+9= 24

3rd to last sum to 12+11+10 = 33

6+51+15+42+24+33 = 57+57+57 = 171