Given: The sequence is: 36,33,30,27,24,... We need to find the maximum value of the sum of the numbers. This is an arithmetic progression (AP) where: First term (a)=36 Common difference (d)=33−36=−3 The sum of n terms of an AP is given by: Formula used: Sum(Sn)=
n
2
[2a+(n−1)d] Calculation: We need to find the maximum value of the sum. The AP ends when the last term becomes ≥0. Last term (l) =a+(n−1)d For the last term to be ≥0 : ⇒36+(n−1)(−3)≥0 ⇒36−3(n−1)≥0 ⇒36−3n+3≥0 ⇒39−3n≥0 ⇒3n≤39 ⇒n≤13 Thus, the sequence has a maximum of n=13 terms. Now, calculate the sum of these 13 terms: S13=
