In an Arithmetic Progression $T_{7} = 18$ and $T_{18} = 7$ , obtain $T_{25}$ .

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Solution

Here $T_{7} = 18$ $T_{18} = 7$
$d = \frac{T_{m} - T_{n}}{m - n}$
$d = \frac{T_{18} - T_{7}}{18 - 7} = \frac{7 - 18}{11} = - 1$
Now,
$T_{7} = 18$
$\Rightarrow a + 6 d = 18$
$\Rightarrow a + 6 (- 1) = 18$
$\Rightarrow$ $a = 24$
Now,
$T_{25} = a + 24 d$
$= 24 - 24$
$= 0$
Thus, $T_{25} = 0$

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