JEE MAIN - Mathematics (2020 - 9th January Evening Slot - No. 2)
The number of terms common to the two A.P.'s
3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.
Answer
14
Explanation
First A.P. is 3, 7, 11, 15, 19, 23, ..... 407
d1 = 4
Second A.P. is 2, 9, 16, 23, ..... 709
d2 = 7
First common term = 23
Common difference of new A.P using the common terms of the two given A.P's is d = L.C.M. (4, 7) = 28
Last term $$ \le $$ 407
$$ \Rightarrow $$ 23 + (n – 1) (28) $$ \le $$ 407
$$ \Rightarrow $$ n $$ \le $$ 14.7
$$ \therefore $$ n = 14
d1 = 4
Second A.P. is 2, 9, 16, 23, ..... 709
d2 = 7
First common term = 23
Common difference of new A.P using the common terms of the two given A.P's is d = L.C.M. (4, 7) = 28
Last term $$ \le $$ 407
$$ \Rightarrow $$ 23 + (n – 1) (28) $$ \le $$ 407
$$ \Rightarrow $$ n $$ \le $$ 14.7
$$ \therefore $$ n = 14
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