(A) The given $A.P.$ is $\frac{4}{3}, 2, \frac{8}{3}, \frac{10}{3}, \ldots$Here,the first term $a = \frac{4}{3}$.The common difference $d = 2 - \frac{

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(A) The given $A.P.$ is $\frac{4}{3}, 2, \frac{8}{3}, \frac{10}{3}, \ldots$Here,the first term $a = \frac{4}{3}$.The common difference $d = 2 - \frac{4}{3} = \frac{6-4}{3} = \frac{2}{3}$.The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n-1)d$.Substituting the values,we get $T_n = \frac{4}{3} + (n-1)\frac{2}{3}$.$T_n = \frac{4}{3} + \frac{2n}{3} - \frac{2}{3}$.$T_n = \frac{2n + 2}{3}$.

Class 10 Mathematics Arithmetic Progressions nth Term of an AP

Easy

For each of the following $A.P.s$,find the $n^{th}$ term: $\frac{4}{3}, 2, \frac{8}{3}, \frac{10}{3}, \ldots$

A
$T_n = \frac{2n+2}{3}$
B
$T_n = \frac{n+2}{3}$
C
$T_n = \frac{2n-2}{3}$
D
$T_n = \frac{n+4}{3}$

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Arithmetic Progressions

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nth Term of an AP

The $\ldots \ldots \ldots \ldots^{th}$ term of the $A.P.$ $200, 196, 192, \ldots$ is $0$.

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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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Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

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The first term of a finite $A.P.$ is $5$ and its last term is $95$. If the common difference of the $A.P.$ is $5$,then there are $\ldots \ldots \ldots$ terms in the $A.P.$

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If the sum of the $3^{\text{rd}}$ and the $8^{\text{th}}$ terms of an $AP$ is $7$ and the sum of the $7^{\text{th}}$ and the $14^{\text{th}}$ terms is $-3,$ find the $10^{\text{th}}$ term.

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For each of the following $A.P.s$,find the $n^{th}$ term: $\frac{4}{3}, 2, \frac{8}{3}, \frac{10}{3}, \ldots$

Similar Questions

The $\ldots \ldots \ldots \ldots^{th}$ term of the $A.P.$ $200, 196, 192, \ldots$ is $0$.

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

Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

The first term of a finite $A.P.$ is $5$ and its last term is $95$. If the common difference of the $A.P.$ is $5$,then there are $\ldots \ldots \ldots$ terms in the $A.P.$

If the sum of the $3^{\text{rd}}$ and the $8^{\text{th}}$ terms of an $AP$ is $7$ and the sum of the $7^{\text{th}}$ and the $14^{\text{th}}$ terms is $-3,$ find the $10^{\text{th}}$ term.

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