(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

The measures of all the four angles of a quadrilateral form an $A.P.$. If the common difference is $10^{\circ}$,find the measures of all the angles.

Difficult

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For a given $A.P.$,$a=2$ and $d=3$. Then,$S_{30} = \dots$

Medium

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Find the $12^{th}$ term and the $24^{th}$ term of the $A.P.$ $9, 13, 17, \ldots$

Medium

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

Easy

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For the finite $A.P.$ $85, 80, 75, \ldots, -30,$ find the $5^{th}$ term from the end.

Medium

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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

The measures of all the four angles of a quadrilateral form an $A.P.$. If the common difference is $10^{\circ}$,find the measures of all the angles.

For a given $A.P.$,$a=2$ and $d=3$. Then,$S_{30} = \dots$

Find the $12^{th}$ term and the $24^{th}$ term of the $A.P.$ $9, 13, 17, \ldots$

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

For the finite $A.P.$ $85, 80, 75, \ldots, -30,$ find the $5^{th}$ term from the end.

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