Question

An arithmetic sequence has a 10th term of 15 and 14th term of 35. show that the equation (y=mx+b) of this graph equals an =-30+(n-1)5.

Answer 1

The arithmetic sequence follows

`a_n=-30+(n-1)5`

Lets see if the 10th term is 15 by replacing the n for 10

n=10

`a_(10)=-30+(10-1)5`
`a_(10)=-30+(9)5=-30+45=15`

Now, Lets see if the 14th term is 35 by replacing the n for 14

n=14

`a_(14)=-30+(14-1)5`
`a_(14)=-30+(13)5=-30+65=35`Then so, the sequence follows the equation an =-30+(n-1)5.