To find the 99th term of the arithmetic sequence 2, -3, -8,..., we first need to identify the first term and the common difference.
-
The first term \( a_1 \) is given as: \[ a_1 = 2 \]
-
To find the common difference \( d \), we can subtract the first term from the second term: \[ d = a_2 - a_1 = -3 - 2 = -5 \]
Now we have:
- First term \( a_1 = 2 \)
- Common difference \( d = -5 \)
The formula for the \( n \)-th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n-1)d \]
To find the 99th term (\( n = 99 \)): \[ a_{99} = a_1 + (99 - 1)d \] \[ a_{99} = 2 + (98)(-5) \] \[ a_{99} = 2 - 490 \] \[ a_{99} = 2 - 490 = -488 \]
Thus, the 99th term of the sequence is: \[ \boxed{-488} \]