Eleven members of the middle school math club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. they paid their guest speaker $1−a−2−. what is the missing digit a of this 3-digit number?

What this question means is that there is a certain number 1x2 that is divisible by 11.

we can simply see what kind of candidates there are. Let's start with 10*11=110.

now, how much is 11*11? it's 121, so not.

12*11? it's  132, and it fits into the question, and the missing number is 3!

so they each paid 12 dollars and gave 132 dollars to the speaker.

The answer is 26 to 1

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for