A sequence consists of thirteen consecutive two-digit even numbers. If the average of the first five numbers in the sequence is 52, what is the average of all thirteen numbers?
(a) 60
(b) 58
(c) 64
(d) 68
Correct Answer : Option a
Let the first 5 even numbers be:
x, x + 2, x + 4, x + 6, x + 8x
Mean = x+4
Given: x + 4 = 52
⇒x = 48
So, the 13 numbers are from:
48 to 72 (even numbers)
Mean of an arithmetic sequence = Average of first and last terms:
Mean = (48 + 72)/2 = 60
Hence, the correct option is a.
