Question

9) terms is zero. (p #q) 3.* If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero. 1000 is invested at 10 percent simple interest Chor​

Answer 1

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Class 11

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>>If m times the m^th term of an A.P. is e

Question

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If m times the m

th

term of an A.P. is equal to n times n

th

term, show that the (m+n)

th

term of the A.P. is zero.

Medium

Solution

verified

Verified by Toppr

Given,

nth term of AP =t

n

=a+(n−1)d

mth term of AP =t

m

=a+(m−1)d

⇒mt

m

=nt

n

m[a+(m−1)d]=n[a+(n−1)d]

m[a+(m−1)d]−n[a+(n−1)d]=0

a(m−n)+d[(m+n)(m−n)−(m−n)]=0

(m−n)[a+d((m+n)−1)]=0

a+[(m+n)−1]d=0

But t

m+n

=a+[(m+n)−1]d

∴t

m+n

=0