Progression (Sequence and Series)Medium
Question
Let Tr be the r th term of an AP, for r = 1, 2, 3....... if for some positive integers m, n we have Tm = 
and Tm = 
, then Tm equals
and Tm = , then Tm equalsOptions
A.
B.
C.1
D.0
Solution
Let Tm = a + (m - 1)d = 
.....(i)
and Tm = a + (n - 1)d =
.....(ii)
On subtracting Eq. (ii) form Eq. (i), we get
(m - n)d =
⇒ d = 
Again, Tm = a + (mn - 1)d
= a + (mn - n + n - 1)d
= a + (n - 1)d + (mn - n)d
Tn + n(m - 1)
= 1
.....(i)and Tm = a + (n - 1)d =
.....(ii)On subtracting Eq. (ii) form Eq. (i), we get
(m - n)d =
⇒ d = Again, Tm = a + (mn - 1)d
= a + (mn - n + n - 1)d
= a + (n - 1)d + (mn - n)d
Tn + n(m - 1)
= 1Create a free account to view solution
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