Question

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

Answer 1

Answer:
`a_n=5+n`

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`

Answer 2

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