If a1 = 12×5, a2 = 15×8, a3 = 18×11, ......, then a1 + a2 + a3 + .... + a100 is
Explanation:
a1 = 12×5 = 1332×5 = 135-22×5 = 1312-15
Similarly, a2 = 1315-18
a3 = 1318-111 and so on till
a100 = 131299-1302 [First term of a100 = 2 + (100 - 1) × 3 = 299]
Now if we add a1, a2, a3, ...., a100
a1 + a2 + a3 + ... + a100 = 1312-15 + 1315-18 + 1318-111 + ... + 131299-1302
= 1312-15+15-18+18-111+...+1299-1302
Terms 15, 18, ... 1296, 1299 will all cancel out
⇒ a1 + a2 + a3 + ... + a100 = 1312-1302
So a1 + a2 + a3 + ... + a100 = 150906 = 25151
Hence, option (a).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.