Final answer:
To check if -150 is a term of the arithmetic progression (AP) 11, 8, 5, 2..., we can use the formula for the nth term of an AP. Using the formula, we find that -150 is not a term in this AP.
Step-by-step explanation:
The given sequence is 11, 8, 5, 2....
To check if -150 is a term of this arithmetic progression (AP), we can use the formula for the nth term of an AP:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, and d is the common difference.
Let's substitute the given values into the formula:
- a1 = 11
- d = -3 (since the common difference between consecutive terms is -3)
- an = -150
Now, solve for n in the equation:
an = a1 + (n-1)d
-150 = 11 + (n-1)(-3)
-150 - 11 = -3n + 3
-161 = -3n + 3
-161 - 3 = -3n
-164 = -3n
-164/-3 = n
n = 54.67
The value for n is not a whole number, which means -150 is not a term in the given arithmetic progression.