Question

The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence.

Answer 1

f(n) = -3n + 23

Explanation:

Answer 2

The rule of an arithmetic sequence:

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

`a_1` - first term

`d` - a difference
`d=a_n-a_(n-1)`

We have:

`a_1=20;\ a_2=17;\ a_3=14;\ a_4=11;\ a_5=8;\ ...`

`a_1=20;\ d=a_2-a_1\to d=17-20=-3`

substitute:

`a_n=20+(n-1)\cdot(-3)=20-3n+3=-3n+23`

Answer: f(n) = -3n + 23