Question

If the number of terms n in one Ap is odd then which term is it's middle point
a. n/2 th
b. (n/2+1)th
c. (n+1/2)th
d. (n-1/2)th​

Answer 1

Answer:

Let, common difference=d

r

th

term =t

r

1

st

term= a

Now m

th

term= t

m

=a+(m−1)d

Since, t

m

=

n

1

Therefore,

n

1

=a+(m−1) …… (1)

Now n

th

term t

n

=a+(m−1)d

Given ,t

n

=

m

1

Therefore,

m

1

=a+(n−1) …… (2)

Subtract equation (2) from equation(1)

n

1

−

m

1

=(m−1)d−(n−1)d

mn

m−n

=(m−n)d

d=

mn

1

Put value d in equation (1)

n

1

=a+(m−1)

mn

1

n

1

=a+

mn

m

+

mn

1

n

1

=a+

n

1

−

mn

1

n

1

=a+

n

1

−

mn

1

a=

mn

1

Now mn

th

term ,

t

mn

=

mn

1

+(mn−1)

mn

1

=

mn

1

+1−

mn

1

t

mn

=1