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:
![a_n = a_1 + (n-1)d](/tpl/images/1354/8797/2c956.png)
In which
is the first term.
−4,−21,−38
First term -4, so ![a_1 = -4](/tpl/images/1354/8797/f85a2.png)
Common difference of ![d = -38 - (-21) = -21 - (-4) = -17](/tpl/images/1354/8797/d7231.png)
Thus
![a_n = a_1 + (n-1)d](/tpl/images/1354/8797/2c956.png)
![a_n = -4 - 17(n-1)](/tpl/images/1354/8797/5d223.png)
Find the 64th term of the arithmetic sequence
This is
. So
![a_n = -4 - 17(n-1)](/tpl/images/1354/8797/5d223.png)
![a_{64} = -4 - 17(64-1) = -4 - 1071 = -1075](/tpl/images/1354/8797/499d2.png)
The 64th term of the arithmetic sequence is -1075.