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Find the number of terms common to the two arithmetic progression 5,9,13,17,…,216 and 3,9,15,21,…..,321

Answer» Correct Answer - 18
The first common term in two Aps is 9.
LCm of their common difference = LCM (4,6) =12
New AP of common elements is 9,21,33,45,….,
Let is contain n terms. Then,
` T_(n) gt 216 Rightarrow 9 + ( n-1) xx 12 le 216 Rightarrow (n-1) xx 12 ge 207`
` Rightarrow (n-1) xx 12 = 204 Rightarrow n =18`
So, there are 18 common terms in two APs.


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