Answer:

Let S

m and S n

be the sum of the first m and first n terms of the AP respectively. Let, a be the first term and d be a common difference

S n

S m

=

m

2

⇒

2

n

[2a+(n−1)d]

2

m

[2a+(m−1)d]

=

n

2

m

2

⇒

2a+(n−1)d

2a+(m−1)d

=

n

m

⇒n[2a+(m−1)d]=m[2a+(n−1)d]

⇒2an+mnd−nd+2am+mnd−nd

⇒md−nd=2am−2an

⇒(m−n)d=2a(m−n)

⇒d=2a

Now, the ratio of mth and nth terms is

a

n

a

m

=

a+(n−1)d

a+(m−1)d

=

a+(n−1)2a

a+(m−1)2a

=

a(1+2n−2)

a(1+2m−2)

=

2n−1

2m−1

Thus, ratio of its mth and nth terms is 2m−1:2n−1

Answer:

Iron nails lose their shiny appearance because an insoluble layer of copper is formed on the nails, Meanwhile, the solution,CuSO4  loses its blue color because of the formation of FeSO4.

Fe + CuSO4 → Cu + FeSO4