Question

Examine the sequence of values below. 8.3, 11.9, 15.5, 19.1, 22.7, 26.3 Which algebraic expression represents the nth value in this sequence?

Answer 1

Add 3.6 to each number.
Ninth would be 37.1. You're welcome!

Answer 2

`\text{Consider the sequence}\\ \\ 8.3,\ 11.9,\ 15.5,\ 19.1,\ 22.7,\ 26.3\\ \\ \text{observe that the difference between two consecutive terms}\\ \text{in the sequence is 3.6}\\ \text{as, }11.9-8.3=15.5-11.9=19.1-15.5=3.6\\ \\ \text{so the given sequence is an Arithmatic sequence with first term, }a_1=8.3\\ \text{and common ratio is }d=3.6\\ \\ \text{hence the nth term of the sequence is given by}\\ \\ a_n=a_1+(n-1)d`

`\Rightarrow a_n=8.3+(n-1)(3.6)\\ \\ \Rightarrow a_n=8.3+3.6n-3.6\\ \\ \Rightarrow a_n=3.6n+4.7`

Hence the algebraic expression that represents the nth value in this sequence is: 3.6n+4.7