Answer :
Consider we need to find the first five terms of the given AP and the explicit formula.
Given:
[tex]a_n=a_{n-1}-3[/tex] when [tex]a_1=5[/tex]
To find:
First five terms of the given AP and the explicit formula.
Solution:
We have,
[tex]a_n=a_{n-1}-3[/tex] ...(i)
[tex]a_1=5[/tex], it means first term is 5.
Putting n=2 in (i), we get
[tex]a_2=a_{2-1}-3[/tex]
[tex]a_2=a_{1}-3[/tex]
[tex]a_2=5-3[/tex]
[tex]a_2=2[/tex]
Second term is 2. So, common difference is
[tex]d=a_2-a_1[/tex]
[tex]d=2-5[/tex]
[tex]d=-3[/tex]
First terms is 5 and common difference is -3. So, the first five terms of the AP are 5, 2, -1, -4, -7.
The explicit formula of an AP is
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_n=5+(n-1)(-3)[/tex]
[tex]a_n=5-3n+3[/tex]
[tex]a_n=8-3n[/tex]
Therefore, the explicit formula of AP is [tex]a_n=8-3n[/tex].