For an AP Sm=20 and Sn=10 …
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Posted by Sagar Maheshwari 7 years, 2 months ago
- 1 answers
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Naveen Sharma 7 years, 2 months ago
\(I \space think \space in \space question S_m = 10 \space and \space S_n = 20 \)
Ans. Given : \(S_m = 10 \)
\(S_n = 20 \space \space \space \space ..... (1) \)
=> n-m = 1
=> m = n-1
The sum of m terms i.e (n-1) terms
\(S_{n-1} =S_m = 10 \space \space \space \space \space \space ...... (2) \)
=> \(n^{th} term = S_n - S_{n-1}\)
=>\(n^{th} term = 20 - 10 = 10\)
=> \(a + (n-1)d = 10\)
=> \(a + (n-1)a = 10 \space \space \space \space \space [as \space a =d ] \)
=> \(a+ na -a = 10 \)
=> \(na = 10 \)
=> \(n = {10\over a}\)
Hence proved
1Thank You