To find the fourth term of an arithmetic sequence, we typically use the formula for the nth term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n - 1)d \][/tex]
where:
- [tex]\( a_n \)[/tex] is the nth term of the sequence,
- [tex]\( a_1 \)[/tex] is the first term of the sequence,
- [tex]\( d \)[/tex] is the common difference,
- [tex]\( n \)[/tex] is the term number.
In this problem:
- The first term [tex]\( a_1 = 10 \)[/tex],
- The common difference [tex]\( d = -7 \)[/tex],
- The term number [tex]\( n = 4 \)[/tex].
Now, let's substitute these values into the formula:
[tex]\[ a_4 = 10 + (4 - 1)(-7) \][/tex]
First, calculate the expression inside the parentheses:
[tex]\[ 4 - 1 = 3 \][/tex]
Next, multiply this result by the common difference:
[tex]\[ 3 \times (-7) = -21 \][/tex]
Finally, add this result to the first term:
[tex]\[ a_4 = 10 + (-21) \][/tex]
This simplifies to:
[tex]\[ a_4 = 10 - 21 = -11 \][/tex]
Thus, the fourth term of the sequence is [tex]\( -11 \)[/tex].
