First slide

Arithmetic progression

Question

The largest term common to the sequences 1, 11, 21, 31…….. to 100 terms and 31, 36, 41, 46……. to 100 terms is

Moderate

A

381
B

471
C

281
D

521

Solution

100th term 1, 11, 21, 31, ….. is 1+ (100 -1) 10 = 991.
100th term of 31, 36, 41, 46…. Is 31+ (100-1) 5 = 526.
Let the largest common term be 526. Then,526 = 31+(n-1) 10 $\Rightarrow n = 50.5$
But n is an integer, hence n=50. Hence , the largest common term is $31 + (50 - 1) 10 = 521$

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