Question

Which of the following sequences are arithmetic sequences for n=1,2,3,___________?

Answer 1

The sequences that are arithmetic for n = 1, 2, 3 are 1, 4 and 1, 4, 7, respectively.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To determine if a sequence is arithmetic for a given value of n, we can substitute the value of n into the expression representing the sequence and check for a consistent difference.

Let's consider the given sequence:

1, 4, 7, 10, ...

For n = 1, the sequence is 1, which is not arithmetic.

For n = 2, the sequence is 1, 4, which is arithmetic with a common difference of 3.

For n = 3, the sequence is 1, 4, 7, which is arithmetic with a common difference of 3.

Therefore, the sequences that are arithmetic for n = 1, 2, 3 are 1, 4 and 1, 4, 7, respectively.