Prove that a_{m + n} + a_{m - n}  =2a_m

Ans:    a _{m + n} = a₁ + (m + n - 1) d

a _m-n = a₁ + (m - n -1) d

a_m = 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]

=          2a_m.       Hence proved.

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

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