CBSE Class 10 Answered
Prove that in any AP am+n +am-n =2am
Asked by prasadmorab000 | 11 Oct, 2020, 08:18: PM
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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