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If (m+1)th term of an A.P. …

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If (m+1)th term of an A.P. is twice the (n+1)th term,prove that(3n+1)th term is twice the (m+n+1)th term.

Posted by Rupesh Sahoo 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

Given,
a_m+1 = 2a_n+1
{tex}\Rightarrow{/tex} a + (m + 1 - 1)d = 2[a + (n + 1 - 1)d]
{tex}\Rightarrow{/tex} a + md = 2[a + nd]
{tex}\Rightarrow{/tex} a + md = 2a + 2nd
{tex}\Rightarrow{/tex} md - 2nd = 2a - a
{tex}\Rightarrow{/tex} md - 2nd = a ..........(i)
To prove:
a_3m+1 = 2a_m+n+1
Proof:
LHS
= a_3m+1
= a + (3m + 1 - 1)d
= a + 3md
= md - 2nd + 3md [From (i)]
= 4md - 2nd
RHS
= 2a_m+n+1
= 2[a + (m + n + 1 -1)d]
= 2[a + md - nd]
= 2[md - 2nd + md + nd] [From (i)]
= 2[2md - nd]
= 4md - 2nd
Hence, LHS = RHS

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