Question

Find an explicit formula for the arithmetic sequence 12, 5, -2, -9..

Answer 1

Answer: $f(n)=19-7n$  

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by :-

$f(n)=a+(n-1)d$                  (1)

, where a = first term

d= common difference

n= number of term

The given arithmetic sequence =  12, 5, -2, -9..

First term : a = 12

Common difference : d= 5-12=-7   [Difference between any two consecutive terms.]

Put a = 12 and d= -7 in (1) , we get

$f(n)=12+(n-1)(-7)$    

Hence, the explicit formula for the given arithmetic sequence : $f(n)=12+(n-1)(-7)$    

We we solve it further , we get

$f(n)=12-7n+7$    

$f(n)=19-7n$    

Required explicit formula :  $f(n)=19-7n$  

Answer 2

T(n)=19-7n
You can use this formula to check if I’m right or wrong by plugging the term # for n...it will show you the # of the term