prove that am n am - n 2amans a, Mathematics

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prove that am n am - n 2amans a

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]

= 2a_m. Hence proved.

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Mathematics: prove that am n am - n 2amans a

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Mathematics: prove that am n am - n 2amans a

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