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In a sequence of consecutive numbers the sum of the first half of the

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In a sequence of consecutive numbers the sum of the first half of the  [#permalink]

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New post 26 Nov 2017, 08:52
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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

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Re: In a sequence of consecutive numbers the sum of the first half of the  [#permalink]

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New post 26 Nov 2017, 09:11
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Option D

Let n be the first number. The sum of first 7 numbers are 7n+21=196.
Hence n=25. Now the last 7 numbers are 7n+(7+8+9+10+11+12+13)=245


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Re: In a sequence of consecutive numbers the sum of the first half of the  [#permalink]

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New post 26 Nov 2017, 09:22
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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



hi..

various ways to do it..

1) average..
consecutive numbers so average will be the middle number = \(\frac{196}{7}=28\)
average of next half = \(28+7=35\), so SUM of these numbers = \(35*7=245\)

2) Sum of each number..
first of 1st half will be 7 less than first of 2nd half
second of 1st half will be 7 less than second of 2nd half and so ontill
seventh of 1st half will be 7 less than first of 2nd half..
total of 2nd half therefore will be 7*7 more than SUM of 1st half ..
sum = 196+49=245

D
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In a sequence of consecutive numbers the sum of the first half of the  [#permalink]

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New post 26 Nov 2017, 10:43
1
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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In a sequence of consecutive numbers the sum of the first half of the &nbs [#permalink] 26 Nov 2017, 10:43
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