(B) The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n-1)d$.Given $T_7 = 108$ and $T_{11} = 212$.The common difference $d$ is calculated

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(B) The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n-1)d$.Given $T_7 = 108$ and $T_{11} = 212$.The common difference $d$ is calculated as $d = \frac{T_{11} - T_7}{11 - 7} = \frac{212 - 108}{4} = \frac{104}{4} = 26$.Now,using the formula $T_n = T_7 + (n - 7)d$:$T_n = 108 + (n - 7) \times 26$.$T_n = 108 + 26n - 182$.$T_n = 26n - 74$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Easy

The $7^{th}$ term of an $A.P.$ is $108$ and the $11^{th}$ term is $212$. Then,its $n^{th}$ term is $\ldots \ldots \ldots \ldots$

A
$74$
B
$26n-74$
C
$-74$
D
$26n$

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Arithmetic Progressions

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Mix Examples - Arithmetic Progressions

For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$

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The sum of how many terms of the $A.P.$ $54, 51, 48, \dots$ is $513$? Explain the reason for getting two different answers.

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The sum of the first $16$ terms of the $A.P.$ $1, 1.5, 2, \ldots$ is:

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For each of the following $A.P.s$,find the $n^{th}$ term: $27, 22, 17, 12, \ldots$

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For an $A.P.$,the $7^{th}$ term is $34$ and the $13^{th}$ term is $64$. Then,the $18^{th}$ term of the $A.P.$ is........

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The $7^{th}$ term of an $A.P.$ is $108$ and the $11^{th}$ term is $212$. Then,its $n^{th}$ term is $\ldots \ldots \ldots \ldots$

Similar Questions

For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$

The sum of how many terms of the $A.P.$ $54, 51, 48, \dots$ is $513$? Explain the reason for getting two different answers.

The sum of the first $16$ terms of the $A.P.$ $1, 1.5, 2, \ldots$ is:

For each of the following $A.P.s$,find the $n^{th}$ term: $27, 22, 17, 12, \ldots$

For an $A.P.$,the $7^{th}$ term is $34$ and the $13^{th}$ term is $64$. Then,the $18^{th}$ term of the $A.P.$ is........

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