Question

Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. 1, 4, 7, 10, . . .

Answer 1

Option a: add 3 to the previous term; 13, 16

Explanation:

The sequence is 1, 4, 7, 10, ....

We need to determine the next two terms of the sequence.

Hence to find the next two terms, first we shall find the common difference between every two terms.

Common difference between 1 and 4 = $4-1=3$

Similarly, common difference between 4 and 7 = $7-4=3$

Common difference between 7 and 10 = $10-7=3$

Hence, the common difference is 3.

So, the next two terms will also have the same common difference 3.

To determine the next two terms, first we shall add 3 to the term 10, we get,

$10+3=13$

Similarly, adding 3 to the term 13, we get,

$13+3=16$

Thus, the sequence is 1, 4, 7, 10, 13, 16, .....

Thus, add 3 to the previous term; 13, 16

Hence, option a is the correct answer.