Let T r be the r th term of A-P for r -1-2-3 - - If for some positive integer m and n we have T m -1-n and T n -1- m- then T mnA- 1B- 1-m-1-nC- 1D- 0

The correct option is C Let a, a + d, a + 2d, . . .. be the A.P T_m = 1/n⇒ a + (m 1)d = 1/n, T_n ⇒1/m⇒ a + (n 1) d = 1/m Solving a = d = 1/mn, Tmn = a+ (mn ...

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Byju's Answer

Standard XII

Mathematics

Sufficient Condition for an Extrema

Let T r be th...

Question

Let $T_{r}$ be the $r^{t h}$ term of A.P for r = 1, 2, 3…. If for some positive integer m and n we have $T_{m} = \frac{1}{n} a n d T_{n} = \frac{1}{m}$ , then $T_{m n}$

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Solution

The correct option is C

Let a, a + d, a + 2d, . . .. be the A.P

$T_{m} = \frac{1}{n} \Rightarrow a + (m - 1) d = \frac{1}{n}, T_{n} \Rightarrow \frac{1}{m} \Rightarrow a + (n - 1) d = \frac{1}{m} S o l v i n g a = d = \frac{1}{m n}, T m n = a + (m n - 1) d = \frac{1 + m n - 1}{m n} = 1$

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