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Short Quiz - Chapter 5 Class 10 Arithmetic Progressions

Chapter 5 Class 10 Arithmetic Progressions | 5 questions

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Question 1 of 5
Question 1 of 5
NCERT Exemplar
The \(11^{\text {th }}\) term of the AP: \(-5, \frac{-5}{2}, 0, \frac{5}{2}, \ldots\) is

Correct option: B

Answer: Here,

$$ a=-5 $$


Common difference:

$$ \begin{gathered} d=-\frac{5}{2}-(-5) \\ d=-\frac{5}{2}+5 \\ d=-\frac{5}{2}+\frac{10}{2} \\ d=\frac{5}{2} \end{gathered} $$


Now,

$$ \begin{gathered} a_{11}=a+(11-1) d \\ a_{11}=-5+10\left(\frac{5}{2}\right) \\ a_{11}=-5+25 \\ a_{11}=20 \end{gathered} $$


20

Answer: (B) \(\mathbf{2 0}\)

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Question 2 of 5
What is the common difference of an AP in which \(a_{18}-a_{14}=32\) ?

Correct option: A

Answer: $$ \begin{aligned} & a_{18}=a+17 d \\ & a_{14}=a+13 d \end{aligned} $$


Subtract:

$$ \begin{gathered} a_{18}-a_{14}=(a+17 d)-(a+13 d) \\ a_{18}-a_{14}=4 d \end{gathered} $$


Given:

$$ \begin{gathered} 4 d=32 \\ d=8 \\ 8 \end{gathered} $$


Answer: (A) 8

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Question 3 of 5
NCERT Exemplar
The first four terms of an AP, whose first term is -2 and the common difference is -2 , are

Correct option: C

Answer: First term:

$$ a=-2 $$


Second term:

$$ a+d=-2+(-2)=-4 $$


Third term:

$$ a+2 d=-2+2(-2)=-6 $$


Fourth term:

$$ a+3 d=-2+3(-2)=-8 $$


So the first four terms are:

$$ -2,-4,-6,-8 $$


Answer: (C)

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Question 4 of 5
NCERT Exemplar
The list of numbers \(-10,-6,-2,2, \ldots\) is

Correct option: B

Answer: Find the common difference:

$$ \begin{gathered} -6-(-10)=4 \\ -2-(-6)=4 \\ 2-(-2)=4 \end{gathered} $$


The difference is constant.
So it is an AP with:

$$ \begin{gathered} d=4 \\ \text { an AP with } d=4 \end{gathered} $$


Answer: (B)

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Question 5 of 5
If the first term of an AP is -5 and the common difference is 2 , then the sum of the first 6 terms is

Correct option: A

Answer: Here,

$$ \begin{gathered} a=-5, d=2, n=6 \\ S_n=\frac{n}{2}[2 a+(n-1) d] \\ S_6=\frac{6}{2}[2(-5)+(6-1)(2)] \\ S_6=3[-10+5(2)] \\ S_6=3[-10+10] \\ S_6=3(0) \\ S_6=0 \\ 0 \end{gathered} $$


Answer: (A) 0

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