Question

3.
Let T, be the T, be the 7th term of an AP. Whose first term is a and common difference is d. If for some
positive integers m, n with m # n, Tm = 1/n and Tn= 1/mthen a - d equals
m
​

Answer 1

Tm = 1/n

⇒ a + (m - 1)d = 1/n

Tn = 1/m

⇒ a + (n - 1)d = 1/m

Subtracting both we get :

⇒ (n - 1)d - (m - 1)d = 1/m - 1/n

⇒ d (n - 1 - m + 1 ) = (n - m)/mn

⇒ d (n - m) = (n - m)/mn

⇒ d = 1/mn

From Tm = 1/n

⇒ a + (m - 1)d = 1/n

⇒ a + (m - 1)/mn = 1/n

⇒ a = 1/n - (m - 1)/mn

⇒ a = (m - m + 1)/mn

⇒ a = 1/mn

a - d = 1/mn - 1/mn ⇒ 0

0 is the answer .