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

Step-by-step explanation:

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

                 (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

Hence, the explicit formula for the given arithmetic sequence :    

We we solve it further , we get

Required explicit formula :