Practice Questions – Arithmetic Progressions – Class X
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Question 1 of 21
1. Question
What is the \(n^{\text{th}}\) term of an arithmetic progression whose sum to ‘\(n^{\text{th}}\)’ terms is \(2n^2-3n\) ?
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Question 2 of 21
2. Question
Find the sum of \(14\) A.M’s between \(5\) and \(8\).
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Question 3 of 21
3. Question
If \(1^3+2^3+\cdots+m^3=3025\), find \(m\).
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Question 4 of 21
4. Question
What is the sum of ‘\(n\)’ arithmetic means between ‘\(a\)’ and ‘\(b\)’.
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Question 5 of 21
5. Question
Given \(P=3+5+7\cdots \, \text{(n terms)}\) and \(Q=5+8+11+\cdots\) \(\text{(10 terms)}\) . What is the value of ‘\(n\)’ if \(\dfrac{P}{Q}=7\) ?
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Question 6 of 21
6. Question
Find the sum of ‘\(n\)’ terms of the series \(1+(1+2)+(1+2+3)+(1+2+3+4)+\cdots\)
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Question 7 of 21
7. Question
If the \(7^{\text{th}}\) and \(13^{\text{th}}\) term of an AP are \(34\) and \(64\) respectively, then
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Question 8 of 21
8. Question
In an AP \(a_{n}=(7n-1)\) then select option which shows correctly
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Question 9 of 21
9. Question
Find three number in arithmetic progression whose sum is \(3\) and product \(-35\)
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Question 10 of 21
10. Question
What is the value of ‘\(x\)’ if \(2x,\ x+10\) and \(3x+2\) are in arithmetic progression ?
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Question 11 of 21
11. Question
Find the sum of the numbers in between \(1\) and \(1000\) which are divisible by 9.
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Question 12 of 21
12. Question
If \(p\neq q\) and the sequences \(p,\ a,\ b,\ q\) and \(p,\ m,\ n,\ q\) each are in AP, then \(\dfrac{b-a}{n-m}\) is
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Question 13 of 21
13. Question
If the \(t\)th term of an AP is \(s\) and the \(s\)th term of the same AP is \(t\), then \(a_{n}\) is
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(1)
![\text{Given, } \\ \begin{align*} a_{t} & =a+(at-1)d=s \\ \text{and, } a_{s} & =a+(s-1)d=t \end{align*} \\ \text{Now, } \begin{align**} t-s & =a+(s-1)d-a-(t-1)d \\ & =(s-t)d \, \,\text{ [From Eqs (1) and (2)]} \\ & =-(t-s)d \\ \end{align**} \text{So, }\, t-s=-(t-s)d\,\Rightarrow\, d=-1. \\ \text{From Eq (1), we get }\,\, a+(t-1)(-1)=s\,\Rightarrow\, a=s+t-1\\ \text{Now, }\begin{align**} a_{n} &=a+(n-1)d \\ &=s+t-1+(n-1)(-1) \\ &=s+t-1-n+1 \\ &=s+t-n \end{align**}](https://mathsgenii.com/wp-content/uploads/blank.png "Rendered by QuickLaTeX.com")
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Question 14 of 21
14. Question
Sides of a pentagon are an AP, IF the perimeter of the pentagon is \(100\), then the sum of its largest and smallest side is
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Question 15 of 21
15. Question
A sum of \(2000 \$\) is invested at \(4\%\) simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of \(30\) year will be
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Question 16 of 21
16. Question
If the \(5^{\text{th}}\) term of an AP is zero, then \(26^{\text{th}}\) term is ______ the \(12^{\text{th}}\) term.
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Question 17 of 21
17. Question
If \(8\) times and \(8^{\text{th}}\) term of an AP is equal to \(15\) time the \(15^{\text{th}}\) term of that AP, then \(23\)rd term of the same AP is
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Question 18 of 21
18. Question
If the ratio of the sum of \(m^{\text{th}}\) and \(n^{\text{th}}\) terms of an AP is \(1:1\), then which of the following is true ?
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Question 19 of 21
19. Question
If \(n\) is odd and \(S_{n}\) denotes their sum, then the sum of first \(20\) such that numbers will be
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Question 20 of 21
20. Question
If \(18^{\text{th}}\) and \(11^{\text{th}}\) terms of an AP are in the ratio \(3:2\), then its \(29^{\text{th}}\) and \(5^{\text{th}}\) terms are in ratio
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Question 21 of 21
21. Question
The sum of \(n\) terms of two AP’s are in the ratio \(5n+9:9n+6\), then the ratio of their \(18\)th therm is
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![\text{Given, } \\ \begin{align*} a_{t} & =a+(at-1)d=s \\ \text{and, } a_{s} & =a+(s-1)d=t \end{align*} \\ \text{Now, } \begin{align**} t-s & =a+(s-1)d-a-(t-1)d \\ & =(s-t)d \, \,\text{ [From Eqs (1) and (2)]} \\ & =-(t-s)d \\ \end{align**} \text{So, }\, t-s=-(t-s)d\,\Rightarrow\, d=-1. \\ \text{From Eq (1), we get }\,\, a+(t-1)(-1)=s\,\Rightarrow\, a=s+t-1\\ \text{Now, }\begin{align**} a_{n} &=a+(n-1)d \\ &=s+t-1+(n-1)(-1) \\ &=s+t-1-n+1 \\ &=s+t-n \end{align**}](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-b347c0260a32a7ab5e30b9e0c780deda_l3.png "Rendered by QuickLaTeX.com")
![\text{Let the sides of pentagon be, } \\ a-2d,\ a-d,\ a,\ a+d,\ a+2d\\ \text{Given perimeter of pentagon = 100}\\ \text{Therefore, }\, a-2d+a-d+a+a+d+2d=100\, \Rightarrow\, 5a=100\, \Rightarrow\, a=20\\ \text{Then, }\, \begin{align*} a+2d+a-2d & =2a \\ & =2\times20 \,\,\text{ [Put the value of a ]} \\ & =40 \end{align*}](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-853d78c4d258242a5648ef59d2ba456a_l3.png "Rendered by QuickLaTeX.com")
![\text{Given, }\\ \begin{array}{ccc} 8a_{8}=15a_{15} & \Rightarrow & 8[a+(8-1)d]=15[a+(15-1)d]\\ & \Rightarrow & 8(a+7d)=15(a+14d) \\ & \Rightarrow & 8a+56d=15a+210d \\ & \Rightarrow & -7a-154d=0 \\ & \Rightarrow & 7a+154d=0 \\ & \Rightarrow & a+22d=0 \\ & \Rightarrow & a+(23-1)d=0 \, \text{Ans (C)} \end{array}\newline](https://mathsgenii.com/wp-content/ql-cache/quicklatex.com-18e068bd960a83672d8a14e6cad00106_l3.png "Rendered by QuickLaTeX.com")