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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
The sum of first 16 terms of the AP: \(10,6,2, \ldots\) is

Correct option: A

Answer: Here,

$$ \begin{gathered} a=10 \\ d=6-10=-4 \\ n=16 \\ S_n=\frac{n}{2}[2 a+(n-1) d] \\ S_{16}=\frac{16}{2}[2(10)+(16-1)(-4)] \\ S_{16}=8[20+15(-4)] \\ S_{16}=8[20-60] \\ S_{16}=8(-40) \\ S_{16}=-320 \\ -320 \end{gathered} $$


Answer: (A) -320

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Question 3 of 5
If 7 times the \(7^{\text {th }}\) term of an AP is equal to 11 times its \(11^{\text {th }}\) term, then its 18 th term will be

Correct option: D

Answer: Given:

$$ 7 a_7=11 a_{11} $$


Now,

$$ \begin{gathered} a_7=a+6 d \\ a_{11}=a+10 d \end{gathered} $$


So,

$$ \begin{aligned} & 7(a+6 d)=11(a+10 d) \\ & 7 a+42 d=11 a+110 d \end{aligned} $$


Bring like terms together:

$$ \begin{gathered} 7 a-11 a=110 d-42 d \\ -4 a=68 d \\ a=-17 d \end{gathered} $$


Now find \(a_{18}\) :

$$ a_{18}=a+17 d $$


Substitute \(a=-17 d\) :

$$ \begin{gathered} a_{18}=-17 d+17 d \\ a_{18}=0 \\ 0 \end{gathered} $$


Answer: (D) 0

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Question 4 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 5 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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