Latest CTS Aptitude Question SOLUTION: Q. If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ? Option A) 1 B) m C) n D) 0

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Q. If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
Option
A) 1
B) m
C) n
D) 0

Asked In CTS Soumya Ranjan Sahoo (10 years ago)

Solved Akanksha Mishra Read Solution (1)

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Read Solution (1) :

Akanksha Mishra  (10 years ago)

mth term of an A.P.
Am = a + (m-1)d
nth term of an A.P.
An = a + (n+1)d

[here a= First term of an A.P
d= difference between two consecutive terms
Am= mth term of A.P.]
According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m^2d-md = an + n^2d - nd
a(m-n)+ (m^2-n^2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0
So Am+n = 0
so answer will be 0

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