NIMCET 2025 Paper

We want to check which number of rows cannot form a decreasing-by-3 sequence whose sum is 630 .
A decreasing-by- 3 sequence for n rows looks like:
a,(a−3),(a−6),...,(a−3(n−1))
Sum of n rows:
S=‌

n

2

[2a−3(n−1)]=630
We test each option to see if it gives a positive integer value of a.
Check n=3
‌

3

2

(2a−6)=630
2a−6=420‌‌⇒‌‌2a=426⇒a=213
✓ Valid (integer)
Check n=4
2(2a−9)=630
2a−9=315⇒2a=324⇒a=162
✓ Valid (integer)
Check n=5
‌

5

2

(2a−12)=630
2a−12=252⇒2a=264⇒a=132
✓ Valid (integer)
Check n=6
3(2a−15)=630
2a−15=210⇒2a=225⇒a=112.5
x Not an integer → impossible