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Formula for sum of arithmetic sequence

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by prachich1987 » Thu Jan 13, 2011 12:52 am
Hi,

I just wanted to confirm whether below formula is right.

In an arithmetic sequence sum of all the terms=median*no. of terms ...irrespective of whether the sequence consists of even no. of terms or odd no. of terms.

Thanks!
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by Anurag@Gurome » Thu Jan 13, 2011 1:22 am
prachich1987 wrote:Hi,

I just wanted to confirm whether below formula is right.

In an arithmetic sequence sum of all the terms=median*no. of terms ...irrespective of whether the sequence consists of even no. of terms or odd no. of terms.

Thanks!
Yes the formula is correct.
This is because, Sum of all terms = (Arithmetic Mean)*(Number of terms), and for arithmetic sequences, the median is equal to the arithmetic mean.
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by prachich1987 » Thu Jan 13, 2011 1:35 am
Anurag@Gurome wrote:
prachich1987 wrote:Hi,

I just wanted to confirm whether below formula is right.

In an arithmetic sequence sum of all the terms=median*no. of terms ...irrespective of whether the sequence consists of even no. of terms or odd no. of terms.

Thanks!
Yes the formula is correct.
This is because, Sum of all terms = (Arithmetic Mean)*(Number of terms), and for arithmetic sequences, the median is equal to the arithmetic mean.
Thanks Anurag!
I think there is one more formula for calculating the sum using first and last term of the sequence.
Can you please advise?
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by Anurag@Gurome » Thu Jan 13, 2011 1:54 am
prachich1987 wrote:I think there is one more formula for calculating the sum using first and last term of the sequence.
Can you please advise?
Sum of all terms of an arithmetic series = (Arithmetic mean of first and last terms)*(Number of terms)
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by prachich1987 » Thu Jan 13, 2011 2:00 am
Anurag@Gurome wrote:
prachich1987 wrote:I think there is one more formula for calculating the sum using first and last term of the sequence.
Can you please advise?
Sum of all terms of an arithmetic series = (Arithmetic mean of first and last terms)*(Number of terms)
Thanks Anurag !
So we can conclude that for any arithmetic sequence,median=Arithmetic mean of first and last terms=Arithmetic mean of middle two terms (for even no. of terms)
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by Anurag@Gurome » Thu Jan 13, 2011 2:05 am
prachich1987 wrote:So we can conclude that for any arithmetic sequence,median=Arithmetic mean of first and last terms=Arithmetic mean of middle two terms (for even no. of terms)
We can conclude much more than this. :)
Refer to my post here: https://www.beatthegmat.com/averages-t73061.html#330653
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