Bunuel wrote:
In a sequence of consecutive numbers the sum of the first half of the numbers is 196. If there are 14 numbers in the set, what is the sum of the second half of the numbers?
A. 201
B. 206
C. 210
D. 245
E. 266
With 14 consecutive integers, the first half of the numbers are terms 1 through 7. Sum of these first seven = 196
For consecutive integers,
First term = n
Seventh term = n + 6
Sum of first half of numbers:
(Average)(# of terms) = Sum
Average = \(\frac{(First Term+LastTerm)}{2}\)
\(\frac{(n + n + 6)}{2} * 7 = 196\)
\((2n + 6)(7) = 392\)
\(14n + 42 = 392\)
\(14n = 350\)
\(n = 25\)
Second half of numbers = terms 8 to 14
8th term: (n+7) = (25+7) = 32
14th term: (n+13)=(25+13) = 38
Sum of second half of numbers, from 32 to 38:
\(\frac{32 + 38}{2}*(7)=(35*7)=245\)
Answer D
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