Formula for sum of arithmetic sequence

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prachich1987: Legendary Member; Posts: 752; Joined: Sun Sep 12, 2010 2:47 am; Thanked: 20 times; Followed by:10 members; GMAT Score:700

Formula for sum of arithmetic sequence

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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prachich1987: Legendary Member; Posts: 752; Joined: Sun Sep 12, 2010 2:47 am; Thanked: 20 times; Followed by:10 members; GMAT Score:700

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?

Quote

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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)

Quote

prachich1987: Legendary Member; Posts: 752; Joined: Sun Sep 12, 2010 2:47 am; Thanked: 20 times; Followed by:10 members; GMAT Score:700

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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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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.