The number of common terms to the two sequences 2, 5, 8, 11, …101 and 3, 5, 7, 9, …113 is
Explanation:
By observation we can see the common terms for the two sequences are 5, 11, 17, …
i.e., the common terms form an Arithmetic Progression whose first term is 5 and the common difference is LCM of the common differences of original series i.e., 6.
Let the number of terms in this common series be n.
Last term of this series = 5 + (n - 1) × 6
The highest term of this common series should be less than or equal to the least of last terms of the two series.
i.e., 5 + (n - 1) × 6 ≤ 101
⇒ 6(n - 1) ≤ 96
⇒ n – 1 ≤ 16
⇒ n ≤ 17.
Hence, number of terms in the common series is 17.
Hence, 17.
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.