Prove the arithmetic progressions equation, Mathematics

Prove that am + n + am - n  =2am

Ans:    a m + n = a1 + (m + n - 1) d

a m-n = a1 + (m - n -1) d

am = a1 + (m-1) d

Add 1 & 2

a m+n + a m-n  =   a1+(m+n-1) d+ a1 + (m-n-1)d

=          2a1+(m+n+m-n-1-1)d

=          2a1+ 2(m-1)d

=          2[a1+ (m-1)d]

=          2[a1+ (m-1)d]

=          2am.       Hence proved.

Posted Date: 4/8/2013 5:30:01 AM | Location : United States

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