Question

the last term of an arithmetic sequence is 207, the common difference is 3, and the number of terms is 14. what is the first term.

Answer 1

An arithmetic sequence that has 14 terms and common difference d=3

The last term is x₁₄= 270

To calculate any nth term on an arithmetic sequence you have to do as follows

`x_n=a+d(n-1)`

Where

xₙ is the nth term of the sequence

a is the first term

d is the common difference

(n-1) indicates that you are considering any value of the sequence except the first one

To determine the first term of the sequence you have to write the equation in terms of a

`\begin{gathered} x_n=a+d(n-1) \\ x_n-d(n-1)=a \\ a=x_n-d(n-1) \end{gathered}`

Replace the expression obtained with the information of the sequence