Write a function that represents the sequence 7, 14, 21, 28, ...

a ₙ = 7n

Step-by-step explanation:

This is an arithmetic sequence, the common difference between each term is 14-7 = 21-14 = 28-21 = 7

to the previous term in the sequence addition of 7 gives the next term.

Arithmetic Sequence:

d = 7

This is the formula of an arithmetic sequence.

a ₙ = a₁ + d (n - 1)

Substitute in the values of

a₁ = 7 and d = 7

a ₙ = 7 + 7 (n - 1)

a ₙ = 7 + 7n - 7

a ₙ = 7 - 7 + 7n = 7n

a ₙ = 7n

Step-by-step explanation:

In an arithmetic sequence, consecutive terms differ by a common difference and it is always constant. Looking at the set of numbers,

14 - 7 = 21 - 14 = 28 - 21 = 7

Therefore, it is an arithmetic sequence with a common difference of 7.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1) d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 7

d = 7

The function that represents the sequence would be

Tn = 7 + (n - 1) 7

Tn = 7 + 7n - 7

Tn = 7n