Question : The average of five consecutive odd numbers is 37. What is the sum of the highest and the lowest number?
Option 1: 8
Option 2: 74
Option 3: 41
Option 4: 66
Correct Answer: 74
Solution :
Since it is a sequence of five consecutive terms, it is an arithmetic progression.
Also, the Mid-term of an odd number of terms of an Arithmetic Progression is the Arithmetic Mean.
So, average = 37 = third term of the sequence
So, the first term (least) = 37 – 2 × 2 = 33
and the last term (highest) = 37 + 2 × 2 = 41
$\therefore$ Sum = 41 + 33 = 74
Hence, the correct answer is 74.
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