First slide

Arithmetic progression

Question

Number of identical terms in the sequence 2, 5, 8,11, ... upto 100 terms and 3, 5, 7, 9, 11, ... upto 100 terms, are

Moderate

A

17
B

33
C

50
D

147

Solution

Common terms are 5, 11, 17, ……..
$T_{n} = 5 + (n - 1) 6 = 6 n - 1$
100th term of the first sequence =2+(100-1)3=299
and 100th term of the second sequence =3+(100-1)2=201
$201 > 6 n - 1 \Rightarrow n \leq 33 \frac{2}{3}$
$\Rightarrow n = 33 (∵ n \in N)$

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