Question

The total number of babies born in a country each minute after midnight January 1st can be modeled by the sequence shown in the table below

write a function that represents the arithmetic sequence​

Answer 1

An explicit function that represents the total number of babies born in this country each minute after midnight is
`a_n=5+(n-1)5`

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

`a_n=a_1+(n-1)d`

Where:

• d represents the common difference.
• 
  `a_1` represents the first term of an arithmetic sequence.
• n represents the total number of terms.

Next, we would write an explicit equation for the sequence by using the arithmetic sequence formula;

Common difference, d = succeding term - preceeding term

Common difference, d = 10 - 5 = 15 - 10 = 20 - 15

Common difference, d = 5

Hence, the explicit function that represents this arithmetic sequence (the total number of babies born in this country each minute after midnight) is given by;

`a_n=a_1+(n-1)d\\\\a_n=5+(n-1)5`