Answer:
The 64th term of the arithmetic sequence is -1075.
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term.
−4,−21,−38
First term -4, so [tex]a_1 = -4[/tex]
Common difference of [tex]d = -38 - (-21) = -21 - (-4) = -17[/tex]
Thus
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n = -4 - 17(n-1)[/tex]
Find the 64th term of the arithmetic sequence
This is [tex]a_{64}[/tex]. So
[tex]a_n = -4 - 17(n-1)[/tex]
[tex]a_{64} = -4 - 17(64-1) = -4 - 1071 = -1075[/tex]
The 64th term of the arithmetic sequence is -1075.
