Question

What is the explicit formula for the sequence? 6, 5, 4, 3, 2, . .

Answer 1

This arithmetic sequence has first term 6 and common difference -1. The general formula is
  an = a1 +(n-1)d

For your sequence, this is
  an = 6 +(n-1)*(-1)
  an = 7 - n

Answer 2

Answer: $a_n=5+n$

Step-by-step explanation:

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

$a_n=a+d(n-1)$, where a is the first term , di sthe common difference and n is the number of terms.

The given sequence : 6, 5, 4, 3, 2, . .

Common difference  d = 1

First term = 1

Now, the explicit formula for given arithmetic sequence will be:

$a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n$

Hence, the explicit formula for given arithmetic sequence :  $a_n=5+n$