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

Question

The number of terms common to the two A.P.’s 3, 7, 11, ..., 407 and 2, 9, 16, ..., 709 is ____.

Smart Achievers · Accepted Answer

(2)

$First common term of both the series is 23 and common difference is 7 \times 4 = 28$

$∵$ $Last term \leq 407$ $\Rightarrow 23 + (n - 1) \times 28 \leq 407$

$\Rightarrow (n - 1) \times 28 \leq 384$

$\Rightarrow n \leq \frac{384}{28} + 1$

$\Rightarrow n \leq 14.71$

$Hence, number of terms common are 14$

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