Explanation
To find the maximum possible sum, we treat this sequence as an Arithmetic Progression (AP) where terms decrease until they are no longer positive.
Step 1: Identify the sequence properties
The sequence is 72,69,66,…
Step 2: Determine the number of positive terms (n)
The n-th term is given by the formula:
an=a+(n−1)d
We require a_n > 0:
72 + (n-1)(-3) > 0
72 - 3n + 3 > 0
75 - 3n > 0
75 > 3n
n < 25
The largest integer n satisfying this inequality is n=24. Therefore, there are 24 positive terms.
Step 3: Calculate the 24th term (a24)
a24=72+(24−1)(−3)
a24=72+(23)(−3)
a24=72−69
a24=3
Step 4: Calculate the sum of the sequence (S24)
Using the sum formula Sn=2n[a+an]:
S24=224[72+3]
S24=12×75
S24=900
Correct Answer:
The maximum possible sum of the sequence is 900, which corresponds to Option 1.