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What is the sum of the terms in a certain sequence of consecutive in a

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What is the sum of the terms in a certain sequence of consecutive in a  [#permalink]

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New post 25 Jun 2015, 12:07
7
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A
B
C
D
E

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73% (01:22) correct 27% (01:13) wrong based on 217 sessions

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What is the sum of the terms in a certain sequence of consecutive integers?

(1) The least term in the sequence is 8.

(2) The average of (arithmetic mean) terms is 16.

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What is the sum of the terms in a certain sequence of consecutive in a  [#permalink]

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New post 26 Jun 2015, 05:21
reto wrote:
What is the sum of the terms in a certain sequence of consecutive integers?

(1) The least term in the sequence is 8.

(2) The average of (arithmetic mean) terms is 16.


CONCEPT: To answer this question we need to know any term of the sequence with it's place no. in Sequence and the Number of terms in the sequence

Statement 1: The least term in the sequence is 8.

The least term doesn't tell us about how many terms the sequence has so
NOT SUFFICIENT

Statement 2: The average of (arithmetic mean) terms is 16

Average of the sequence of Consecutive terms = Median of the sequence = Average of Least and Highest term
But The Average of the terms doesn't tell us about how many terms the sequence has so
NOT SUFFICIENT

Combining the two statements

Average of the sequence of Consecutive terms = Median of the sequence = Average of Least and Highest term = (8+ Highest terms)/2 = 16

i.e. Highest term of the Sequence = 32-8 = 24
i.e. The series includes all Integers from 8 to 24 i.e. a total of 17 terms
Now the Sum of the series can be calculated = 16*17 = 272

SUFFICIENT

Answer: option C
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Re: What is the sum of the terms in a certain sequence of consecutive in a  [#permalink]

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New post 24 Dec 2015, 07:38
TO find the sum we need to following

No. of terms and Any one term
Common difference

Since this is a sequence of consecutive integers, the common difference is 1. However, we don't know how many terms or the first term.

Statement 1: The first terms is 8 The last term? 998647? 12? 156?
No clue. Insufficient

Statement 2: Gives the average
In an AP the median and the mean are same. So, if we know the middle term and the number of terms or the first term it is sufficient to make the needed calculations
This statement gives the average.
Could the sequence be 15, 16, 17?
Or could it be 14, 15, 16, 17, 18?
The sum varies.
Insufficient

Botht the statements together give the first term as well as the average, which happens to be the median in a set of consecutive integers. Hence, C
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Re: What is the sum of the terms in a certain sequence of consecutive in a  [#permalink]

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New post 09 May 2017, 08:42
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Re: What is the sum of the terms in a certain sequence of consecutive in a &nbs [#permalink] 09 May 2017, 08:42
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