Question

A chemist heats up several unknown substances to determine their boiling point. Use the table to determine whether the sequence is arithmetic. If it is arithmetic, write an explicit rule and a recursive rule for the sequence. If not, explain why it is not arithmetic.
Substance: 1, 2, 3, 4
Boiling point (°F): 100, 135, 149, 165, 188

Answer 1

Since the difference between consecutive terms is not constant, the sequence is not arithmetic.

In an arithmetic sequence, the difference between consecutive terms is constant, called common difference d.

A recursive formula is given by:

$a_{n+1} = a_{n} + d$

In which $a_1$ is the first term.

In this problem:

• The terms are: 100, 135, 149, 165, 188.
• 135 - 100 = 35, 149 - 135 = 14, that is, the differences are not constant, so this is not an arithmetic sequence.

A similar problem is given at brainly.com/question/23901992