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

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

Answer 2

Answer:

f(n) = -3n + 23

Step-by-step explanation: