Discussion

Explanation:

38, 55, 72, … forms an AP whose first term is 38 and common difference is 17.
∴ Tn = 38 + (n - 1) × 17

To find the average we need to find the highest and lowest 3-digit numbers of this sequence.

Lowest: 38 + (n - 1) × 17 > 99
⇒ 17n - 17 > 61
⇒ 17n > 78
⇒ n > 4
∴ Least possible value of n = 5
⇒ Least such number = 38 + 4 × 17 = 106

Highest: 38 + (n - 1) × 17 < 999
⇒ 17n - 17 < 961
⇒ 17n < 978
⇒ n < 56.5
∴ Highest possible value of n = 56
⇒ Highest such number = 38 + 56 × 17 = 990

∴ The average of the sequence (AP) is same as the average of lowest and highest terms = 106+9902 = 548

Hence, 548.

» Your doubt will be displayed only after approval.


Doubts


Feedback

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.


© 2024 | All Rights Reserved | Apti4All