A mystery number is a factor of 100 and a common multiple
of 2 and 5. The sum of its digits is 5. What is the number?

50

Step-by-step explanation:

The number is a common multiple of 2 and 5, which means it is a multiple of 10.  So the last digit is 0.

The sum of the digits is 5.  The number is a factor of 100, so the only possible solution is 50.

, and

for

step-by-step explanation:

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

note the following:

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