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CBSE Class 10 Answered

Prove that in any AP am+n +am-n =2am
Asked by prasadmorab000 | 11 Oct, 2020, 08:18: PM
answered-by-expert Expert Answer
We need to prove in Arithmetic progression ,  a(m+n) + a(m-n) = 2 am 
 
where an is n-th term in arithmetic progression .
 
Let a1 be first term and d is common difference
 
a(m+n) = a1 + ( m+n-1) d   ...................(1)
 
a(m-n) = a1 + ( m -n -1 ) d  .................(2)
 
By adding above two equations, we get
 
a(m+n) + a(m-n) = 2 [ a1 + ( m-1) d ] = 2 am
Answered by Thiyagarajan K | 14 Oct, 2020, 10:12: PM

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