For any given Arithmetic Progression (A.P.),t | vedclass

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(D) In an Arithmetic Progression $(A.P.)$,the $n^{th}$ term is given by the formula: $T_{n} = a + (n - 1)d$,where $a$ is the first term and $d$ is the

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$\frac{T_{m} - T_{n}}{m - n}$

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(D) In an Arithmetic Progression $(A.P.)$,the $n^{th}$ term is given by the formula: $T_{n} = a + (n - 1)d$,where $a$ is the first term and $d$ is the common difference.For the $m^{th}$ term: $T_{m} = a + (m - 1)d$.For the $n^{th}$ term: $T_{n} = a + (n - 1)d$.Subtracting the two equations:$T_{m} - T_{n} = [a + (m - 1)d] - [a + (n - 1)d]$$T_{m} - T_{n} = (m - 1 - n + 1)d$$T_{m} - T_{n} = (m - n)d$Therefore,the common difference $d$ is given by:$d = \frac{T_{m} - T_{n}}{m - n}$.

For any given Arithmetic Progression $(A.P.)$,the common difference $d$ is equal to:

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