Question types

Sequences and Series question types

36 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

36
Questions
6
Question groups
5
Question types
Sample Questions

Sequences and Series questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the AP, then Sq equals:

  1. $\frac{\text{q}^3}{2}$
  2. mnq
  3. q3
  4. (m + n)q2
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If x, 2y and 3z are in A.P. where the distinct numbers x, y and z are in G.P., then the common ratio of the G.P. is:

  1. $3$

  2. $\frac{1}{3}$

  3. $2$

  4. $\frac{1}{2}$

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The first term of an A.P. is a and the sum of the first p terms is zero, show that the sum of its next q term is $\frac{-\text{a}(\text{p + q})\text{q}}{\text{p}-1}.$
[Hint: Required sum = Sp + q - Sp]
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The sum of interior angles of a triangle is 180°. Show that the sum of the interior angles of polygons with 3, 4, 5, 6,… sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
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Q 163 Marks Question3 Marks
A man saved Rs. 66000 in 20 years. In each succeeding year after the first year he saved Rs. 200 more than what he saved in the previous year. How much did he save in the first year?
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Q 173 Marks Question3 Marks
In a cricket tournament 16 school teams participated. A sum of Rs. 8000 is to be awarded among themselves as prize money. If the last placed team is awarded Rs. 275 in prize money and the award increases by the same amount for successive finishing places, how much amount will the first place team receive?
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Q 183 Marks Question3 Marks
A side of an equilateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. This process is continued for third, fourth, fifth, triangles. Find the perimeter of the sixth inscribed equilateral triangle.
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Q 193 Marks Question3 Marks
A man accepts a position with an initial salary of Rs. 5200 per month. It is understood that he will receive an automatic increase of Rs. 320 in the very next month and each month thereafter.
  1. Find his salary for the tenth month.
  2. What is his total earnings during the first year?
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Q 203 Marks Question3 Marks
If a1, a2, a3, ..., an are in A.P., where ai > 0 for all i, show that:
$\frac{1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_2}}+\frac{1}{\sqrt{\text{a}_2}+\sqrt{\text{a}_3}}+....+\frac{1}{\sqrt{\text{a}_{\text{n}-1}}+\sqrt{\text{a}_\text{n}}}=\frac{\text{n}-1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_\text{n}}}$$$
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In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
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If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is $\Big(\frac{\text{q}^\text{p}}{\text{p}^\text{q}}\Big)^{\frac{1}{\text{p}-\text{q}}}.$
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1f the sum of p terms of an AP. is q and the sum of q terms isp, then show that the sum ofp +q terms is -(p + q). Also, find the sum of first p - q terms (where, p > q).
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A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
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