SOLUTION: Hai Sir, please help me on this problem, i could find the soultion If (m+1)th term of an AP is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term. T

Question 416953: Hai Sir, please help me on this problem, i could find the soultion
If (m+1)th term of an AP is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If (m+1)th term of an AP is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.
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Form those terms and see if the claim is correct
using a(n) = a + (n-1)d.
----
a(m+1) = a + md
===
a(n+1) = a + nd
====
a(3m+1) = a +(3m)d
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a(m+n+1) = a + (m+n)d
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If (m+1)th term of an AP is twice the (n+1)th term, prove that (3m+1)th term is twice the (m+n+1)th term.
---
Condition: a+md = 2(a+nd)
a+md = 2a+2nd
a = md-2nd
----
Prove a+(3m)d = 2[a + (m+n)d]
Substitute for "a" and see if you get an identity.
md-2nd + (3m)d = 2(md-2nd) + 2md + 2nd
4md -2nd = 4md - 2nd
It works!
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Cheers,
Stan H.
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