Answer:
[tex]T_n = -97n[/tex]
Step-by-step explanation:
The actual sequence is: -97, -194, -291, -388
Required
Determine the nth term
nth term of an arithmetic progression is:
[tex]T_n = T_1 + (n - 1)d[/tex]
Where
[tex]T_1 = First\ Term = -97[/tex]
[tex]d = Common\ Difference = -194 - (-97) =-97[/tex]
So:
[tex]T_n = T_1 + (n - 1)d[/tex] becomes
[tex]T_n = -97 + (n - 1) * -97[/tex]
[tex]T_n = -97 -97n + 97[/tex]
Collect Like Terms
[tex]T_n = -97n + 97-97[/tex]
[tex]T_n = -97n[/tex]
Hence, a term of the sequence is:
[tex]T_n = -97n[/tex]
