Question

write an explicit formula for each sequence. 1,4,7,10

Answer 1

is that correct

Answer 2

show your work

Answer 3

The explicit formula for the sequence 1, 4, 7, 10 is:

an = 3n - 2

where n is the position of the term in the sequence.

For example,

a1 = 3(1) - 2 = 1
a2 = 3(2) - 2 = 4
a3 = 3(3) - 2 = 7
a4 = 3(4) - 2 = 10

and so on.

Answer 4

Yes, that is correct.

Answer 5

To find the explicit formula for the sequence 1, 4, 7, 10, we can first observe that the difference between each consecutive term is 3.

So, we can write the difference as:

d = 4 - 1 = 7 - 4 = 10 - 7 = 3

Since the common difference is constant, we know that we are dealing with an arithmetic sequence, and we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.

Now, we can substitute the given values:

a1 = 1
d = 3

So,

an = 1 + (n-1)(3)
= 1 + 3n - 3
= 3n - 2

Therefore, the explicit formula for the sequence 1, 4, 7, 10 is:

an = 3n - 2.