Let's determine the 33rd term of the arithmetic sequence given by the terms: 7, 2, -3, -8.
First, identify the first term of the sequence:
[tex]\[ a_1 = 7 \][/tex]
Next, determine the common difference [tex]\( d \)[/tex]. The common difference [tex]\( d \)[/tex] is found by subtracting the first term from the second term:
[tex]\[ d = a_2 - a_1 = 2 - 7 = -5 \][/tex]
Using the formula for the n-th term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n-1) \cdot d \][/tex]
we need to find the 33rd term ([tex]\( a_{33} \)[/tex]):
[tex]\[ a_{33} = a_1 + (33-1) \cdot d \][/tex]
[tex]\[ a_{33} = 7 + 32 \cdot (-5) \][/tex]
[tex]\[ a_{33} = 7 + 32 \cdot (-5) \][/tex]
[tex]\[ a_{33} = 7 + (-160) \][/tex]
[tex]\[ a_{33} = 7 - 160 \][/tex]
[tex]\[ a_{33} = -153 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{-153} \][/tex]
Among the given options:
A. -158
B. -157
C. -148
D. -147
None of these options are correct because the 33rd term is [tex]\(-153\)[/tex]. The given options do not include the correct answer.
