Number of terms common between two series 2 + 5 + 8 +..... upto 50 terms and series 3 + 5 + 7 + 9...

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8. Sequences and Series

normal

The number of terms common between the two series $2 + 5 + 8 +.....$ upto $50$ terms and the series $3 + 5 + 7 + 9.....$ upto $60$ terms, is

A

$18$

B

$20$

C

$22$

D

$24$

Solution

$2,5,8,11,14,17 \ldots \ldots \ldots .150$

$3,5,7,9,11,13,15,17, \ldots \ldots \ldots 121$

common series $5,11,17, \ldots \ldots \ldots$

$\therefore \mathrm{t}_{\mathrm{n}}=5+(\mathrm{n}-1) 6=6 \mathrm{n}-1$

$\Rightarrow 6 n \leq 122$ $n \leq \frac{122}{6}$

$n \leq 20.2$ $\therefore \mathrm{n}=20$

Standard 11

Mathematics

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