Answer:
[tex]\boxed {a_{24} = - 70}[/tex]
Step-by-step explanation:
According to the following pattern sequence ([tex]-1, -4, -7, -10[/tex] ), it is Arithmetic Sequence, because every negative number is subtracted by [tex]3[/tex]. So, to find the 24th term, you need to use the Arithmetic Sequence Formula and solve to find the 24th term:
[tex]a_{n} = a_{1} + (n - 1) d[/tex]
[tex]a_{n}[/tex]: nth term in the sequence
[tex]a_{1}[/tex]: 1st term
[tex]n[/tex]: term position
[tex]d[/tex]: Common difference
-Apply to the formula:
[tex]a_{24} = -1 - 3 (24 - 1)[/tex]
[tex]a_{n} = a_{24}[/tex]
[tex]a_{1} = -1[/tex]
[tex]n = 24[/tex]
[tex]d = -3[/tex]
-Solve:
[tex]a_{24} = -1 - 3 (24 - 1)[/tex]
[tex]a_{24} = -1 - 3 (23)[/tex]
[tex]a_{24} = -1 - 69[/tex]
[tex]\boxed {a_{24} = - 70}[/tex]
Therefore, the 24th term is [tex]-70[/tex].
