Verified Solution • 2025–26 Session moderate

QJEEM22Ma7799: JEE Main 2022 Mathematics - Class 11 JEEM22Ma7799 Solution: Different A.P.'s are constructed with the first term 100, the…

Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ___________.

Step-by-Step Verified Solution

d1=199−1002∉I{d_1} = {{199 - 100} \over 2} \notin I

d2=199−1003=33{d_2} = {{199 - 100} \over 3} = 33

d3=199−1004∉I{d_3} = {{199 - 100} \over 4} \notin I

dn=199−100i+1∈I{d_n} = {{199 - 100} \over {i + 1}} \in I

di=33+11, 9{d_i} = 33 + 11,\,9

Sum of CD's =33+11+9= 33 + 11 + 9

=53= 53

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring