The number of terms common to the two A.P.'s 3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.
Answer (integer)
14
Solution
First A.P. is 3, 7, 11, 15, 19, 23, ..... 407
<br><br>d<sub>1</sub> = 4
<br><br>Second A.P. is 2, 9, 16, 23, ..... 709
<br><br>d<sub>2</sub> = 7
<br><br>First common term = 23
<br><br>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
<br><br>Last term $\le$ 407
<br><br>$\Rightarrow$ 23 + (n – 1) (28) $\le$ 407
<br><br>$\Rightarrow$ n $\le$ 14.7
<br><br>$\therefore$ n = 14
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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