(C) The $n^{th}$ term of an $A.P.$ is given by $T_{n} = a + (n-1)d$.Given $T_{7} = 12$ and $T_{12} = 72$.The common difference $d$ can be calculated u

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(C) The $n^{th}$ term of an $A.P.$ is given by $T_{n} = a + (n-1)d$.Given $T_{7} = 12$ and $T_{12} = 72$.The common difference $d$ can be calculated using the formula $d = \frac{T_{n} - T_{m}}{n - m}$.Substituting the values: $d = \frac{T_{12} - T_{7}}{12 - 7}$.$d = \frac{72 - 12}{5}$.$d = \frac{60}{5} = 12$.Therefore,the common difference $d$ is $12$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Medium

For a given $A.P.$,$T_{7} = 12$ and $T_{12} = 72$. Then,$d = \dots \dots \dots \dots$

A
$6$
B
$15$
C
$12$
D
$18$

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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

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For a given $A.P.$,$T_{7} = 12$ and $T_{12} = 72$. Then,$d = \dots \dots \dots \dots$

Similar Questions

The fourth composite number in the $A.P.$ $5, 7, 9, 11, \ldots$ is......

For the finite $A.P.$ $1, 4, 7, \ldots, 118,$ find the $15^{th}$ term from the end.

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Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
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$a=\sqrt{2}, d=\frac{1}{\sqrt{2}}$