The largest term common to the sequence 1,11,21,31, to 100 terms and 31,36,41,46, - Maths - Sequences and Series

Question

The largest term common to the sequence 1,11,21,31, to 100 terms
and 31,36,41,46, to 100 terms is (A) 381 (B) 471 (C) 281 (D) none
Please give the solution alse

Anuradha Sharma · Accepted Answer

The first sequence is , 1+11+21+31+41+51+61+71+81+91+
100 term
last term will be = 1+100-1×10=991and for the sequence 31+36+41+46+51+
100 term last term will be = 31+100-1×5=526Now we have the common term as, 31+51+71+
and nth term of this sequence will be=31+n-1×20=20n+11and this will be less than 526So 20n+11<52620n<515n<5152025
75 So n = 25Hence the largest common term = 20×25+11=511

The largest term common to the sequence 1,11,21,31,.... to 100 terms and 31,36,41,46,..... to 100 terms is (A) 381 (B) 471 (C) 281 (D) none . Please give the solution alse.