(B) Given sequence: $0.2, 0.22, 0.222, 0.2222, \ldots$To check if the sequence is an $AP$,we calculate the difference between consecutive terms:$a_{2}

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(B) Given sequence: $0.2, 0.22, 0.222, 0.2222, \ldots$To check if the sequence is an $AP$,we calculate the difference between consecutive terms:$a_{2} - a_{1} = 0.22 - 0.2 = 0.02$$a_{3} - a_{2} = 0.222 - 0.22 = 0.002$$a_{4} - a_{3} = 0.2222 - 0.222 = 0.0002$Since the difference $a_{k+1} - a_{k}$ is not constant,the given sequence does not form an $AP$.

Class 10 Mathematics Arithmetic Progressions Textbook -Arithmetic Progressions

Medium

Are $0.2, 0.22, 0.222, 0.2222, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

A
Yes,$d = 0.02$,next terms are $0.22222, 0.222222, 0.2222222$
B
No,they do not form an $AP$.
C
Yes,$d = 0.2$,next terms are $0.4, 0.6, 0.8$
D
Yes,$d = 0.002$,next terms are $0.22222, 0.222222, 0.2222222$

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Class 10

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Chapter

Arithmetic Progressions

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Textbook -Arithmetic Progressions

Find the sum of the following $APs$: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots,$ to $11$ terms.

Medium

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For the following $APs$,$-5, -1, 3, 7, \ldots$,write the first term and the common difference.

Easy

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In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

Medium

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In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

Easy

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The sum of the $4^{th}$ and $8^{th}$ terms of an $AP$ is $24$ and the sum of the $6^{th}$ and $10^{th}$ terms is $44$. Find the first three terms of the $AP$.

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Are $0.2, 0.22, 0.222, 0.2222, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

Similar Questions

Find the sum of the following $APs$: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots,$ to $11$ terms.

For the following $APs$,$-5, -1, 3, 7, \ldots$,write the first term and the common difference.

In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

The sum of the $4^{th}$ and $8^{th}$ terms of an $AP$ is $24$ and the sum of the $6^{th}$ and $10^{th}$ terms is $44$. Find the first three terms of the $AP$.

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