JEE PYQ: Sequence And Series Question 45
Question 45 - 2020 (09 Jan Shift 2)
The number of terms common to the two A.P.’s 3, 7, 11, $\ldots$, 407 and 2, 9, 16, $\ldots$, 709 is _______.
Show Answer
Answer: (14)
Solution
First common term of both the series is 23 and common difference is $7 \times 4 = 28$
$\therefore$ 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, $n = 14$
BETA
