Question

Find the explicit formula for 5, 9, 13, 17
ASAP​

Answer 1

The explicit formula for the sequence 5, 9, 13, 17 is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

Step-by-step explanation:

The given sequence is 5, 9, 13, 17. To find the explicit formula, we need to determine the pattern or rule that generates these numbers. In this case, the pattern can be observed by adding 4 to the previous term to get the next term. So, the explicit formula for this sequence is:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term (5 in this case), n is the position of the term in the sequence, and d is the common difference (4 in this case).

Using this formula, we can find any term in the sequence by plugging in the values for n and a1.]

Answer 2

aₙ = 4n + 1

Step-by-step explanation:

The terms of your sequence are.

5, 9, 13, 17

This is an arithmetic sequence, because there is a constant difference of 4 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,

aₙ = 5 + 4(n - 1) = 5 + 4n - 4

aₙ = 4n + 1

The explicit formula for sequence is aₙ = 4n + 1.