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Number of identical terms in the sequence 2, 5, 8, 11.... upto

Question

Number of identical terms in the sequence $2, 5, 8, 11....$ upto $100$ terms are

17

33

50

147

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Luna Discussed

Number of identical terms in the sequence

2, 5, 8, 11....

upto

100

terms are

11 mins ago

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11 mins ago

Text solutionVerified

First sequence is

2, 5, 8, 11, .....

upto

100

terms

Here,

n^{t h}

term is

2 + (n - 1) 3

Alternate terms are

5, 11, 17, .....

∴

term of common sequence,

t_{n} = 5 + (n - 1) 6 = (6 n - 1)

Also, 100th term of the first sequence

= 2 + (100 - 1) 3 = 201

\Rightarrow t_{n} \leq 201

\Rightarrow 6 n - 1 \leq 201

\Rightarrow 6 n \leq 202

\Rightarrow n \leq 33 \frac{2}{3}

∴ n = 33

(∵ n \in N)

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Question Text	Number of identical terms in the sequence $2, 5, 8, 11....$ upto $100$ terms are
Answer Type	Text solution:1
Upvotes	150