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Arithmetic Progressions

10th Class - CBSE - Mathematics - 4071 Questions - 0 Concepts

Important Questions

Q1 Subjective Medium
Complete the following activity to find the sum of natural number from $$1$$ to $$140$$ which are divisible by $$4$$
Sum of numbers from $$1$$ to $$140$$, which are divisible by $$4= \Box$$

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Q2 Subjective Medium
$$11, 8, 5, 2,...$$ In this $$A.P.$$ which term is number $$-151$$?

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Q3 Subjective Medium
Which of the following sequences are in arithmetic progression?
$$1/2, 1/3, 1/4, 1/5, .$$

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Q4 Subjective Medium
Which of the following sequences are in arithmetic progression?
$$5, 9, 12, 18, .$$

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Q5 Subjective Medium
Which of the following sequences are in arithmetic progression?
$$15, 12, 9, 6, .$$

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Q6 Subjective Medium
If $$m$$ times the $$m^{th}$$ term of an A.P. is equal to $$n$$ times the $$n^{th}$$ term then show that the $$(m + n)^{th}$$ term of the A.P. is zero .

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Q7 Subjective Medium
If the sum of first $$p$$ terms of an $$A.P$$ is equal to the sum of first $$q$$ terms then show that the sum of its first $$(p+q)$$ terms ia zero $$(p\neq q)$$.

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Q8 Subjective Hard
Find the sum to $$n$$ terms of the series: $$\dfrac{{{1^3}}}{1} + \dfrac{{{1^3} + {2^2}}}{2} + \dfrac{{{1^3} + {2^3} + {3^3}}}{3} + .....$$

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Q9 Subjective Hard
A meeting hall has 20 seats in the first raw, 24 seats in the second row,28 seats in the third row, and so on and has in all 30 rows. How many seats are there in the meeting hall ?

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Q10 Single Correct Hard
Evaluate $$\sum_{r=1}^{n}\left [ \sum_{k=1}^{r}k \right ] \left [ \log_{1/2}\sqrt{(4x-x^{2})} \right ]^{r}$$. Find $$x$$ for which summation is a finite number as $$n\rightarrow \infty $$
  • A. $$x\in \left ( 0,2-\displaystyle \frac{\sqrt{15}}{2} \right )$$
  • B. $$x\in \left ( 0,-2+\displaystyle \frac{\sqrt{15}}{2} \right )$$
  • C. $$x\in \left ( 0,-2-\displaystyle \frac{\sqrt{15}}{2} \right )$$
  • D. $$x\in \left ( 0,2+\displaystyle \frac{\sqrt{15}}{2} \right )$$

Asked in: Mathematics - Arithmetic Progressions


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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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