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...
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. ?
Answer/Solution
0
Steps/Work
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
ANSWER:D
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
ANSWER:D