JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of the common terms of the following three arithmetic progressions. \(3,7,11,15,...................,399\) \(2,5,8,11,............,359\) and \(2,7,12,17,...........,197\), is equal to \(................\).
- A \(322\)
- B \(321\)
- C \(324\)
- D \(328\)
Answer & Solution
Correct Answer
(B) \(321\)
Step-by-step Solution
Detailed explanation
\(3,7,11,15, \ldots \ldots \ldots \ldots, 399 \quad d_1=4\) \(2,5,8,11, \ldots \ldots \ldots \ldots ., 359 \quad d_2=3\) \(2,7,12,17, \ldots \ldots ., 197 \quad d_3=5\) \(\operatorname{LCM}\left(d_1, d_2, d_3\right)=60\) Common terms are \(47, 107, 167\) \(Sum =321\)
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