Answer:
-164
Step-by-step explanation:
The given sequence is: \{-40, -44, -48, -52, ...\}; a_{32}
To find the value of the 32nd term in the sequence, we can observe that each term decreases by 4:
1st term: -40
2nd term: -40 - 4 = -44
3rd term: -44 - 4 = -48
4th term: -48 - 4 = -52
We can represent this pattern mathematically:
The nth term in the sequence can be expressed as:
a_n = a_1 + (n-1)d
Where:
- a_n is the nth term
- a_1 is the first term (-40 in this case)
- d is the common difference (-4 in this case)
Substitute the values into the formula to find the 32nd term:
a_{32} = -40 + (32-1)(-4)
a_{32} = -40 + 31*(-4)
a_{32} = -40 - 124
a_{32} = -164
Therefore, the 32nd term in the sequence is -164.