Anumber is divisible by 3 if the sum of the digits of the number is divisible by 3.

Yes, a number is divisible by 3 if the sum of digits is divisible by 3.

Step-by-step explanation:

The rule of divisibility for three.

The rule for divisibility of three says that if the sum of digits of a number is divisible by 3, then the number itself is divisible by 3.

This is the universally accepted rule for divisibility of three and is always true.

This could be illustrated with the help of examples.

1) 23,657

Since 23 is not divisible by 3, the number is not divisible by 3.

2) 42,789

Since 30 is divisible by 3, 42,789 is divisible by 3.

x

step-by-step explanation:

, 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