vinay1983 wrote:Consider the following sequence : 2,22,222,2222,22222 etc. What is ten's digit of the sum of the first fifty terms of the sequence?
A. 2
B. 8
C. 6
D. 4
E. 0
Let K = the sum of the fifty terms.
To determine the tens digit of K, we need examine only the UNITS DIGITS and the TENS DIGITS of the 50 terms:
02 + 22 + 22 + .... + 22 + 22 + 22.
Note that all of the digits are the same except for one: the TENS digit of the first term = 0.
The sum of the 50 units digits = 50*2 = 10
0.
Thus, the units digit of K = 0.
When we calculate the tens digit of K, we must CARRY 10 from the units place.
The sum of the 50 tens digits + 10 carried from the units place = 0 + 49*2 + 10 = 10
8.
Thus, the tens digit of K = 8.
The correct answer is
B.
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