8. Sequences and Series
hard

The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is

A

$20$

B

$17$

C

$11$

D

$14$

(JEE MAIN-2020)

Solution

Common term are : $23,51,79, \ldots . . T_{n }$ $\mathrm{T}_{\mathrm{n}} \leq 407 \quad \Rightarrow 23+(\mathrm{n}-1) 28 \leq 407$

$\Rightarrow n \leq 14.71$

$\mathrm{n}=14$

Standard 11
Mathematics

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