Question types

Geometric Progressions question types

181 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

181
Questions
5
Question groups
5
Question types
Sample Questions

Geometric Progressions 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 infinite G.P., first term is equal to 10 times the sum of all successive terms, the its common ratio is:
  1. $\frac{1}{10}$
  2. $\frac{1}{11}$
  3. $\frac{1}{9}$
  4. $\frac{1}{20}$
View full solution
If a, b, c are in G.P. and $\text{a}^{\frac{1}{\text{x}}}=\text{b}^{\frac{1}{\text{y}}}=\text{c}^{\frac{1}{\text{z}}},$ then xyz are in:
  1. AP
  2. GP
  3. HP
  4. None of these.
View full solution
The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of original G.P. is:
  1. $\frac12$
  2. $\frac{2}{3}$
  3. $\frac13$
  4. $\frac{-1}{2}.$
View full solution
Q 173 Marks Question3 Marks
If Sp denotes the sum of the series $1+\text{r}^{\text{p}}+\text{r}^{2\text{r}}+\ \dots\text{ to }\infty$ and Sp the sum of the series $1-\text{r}^{\text{p}}+\text{r}^{\text{2p}}-\ \dots\text{ to }\infty,$ prove that $\text{S}_\text{p} + \text{S}_\text{p} = 2 \text{S}_{2\text{p}}.$
View full solution
Q 183 Marks Question3 Marks
If a, b, c are in G.P., prove that:
$\frac{(\text{a}+\text{b}+\text{c})^2}{\text{a}^2+\text{b}^2+\text{c}^2}=\frac{\text{a}+\text{b}+\text{c}}{\text{a}-\text{b}+\text{c}}$
View full solution
One side of equilateral triangle is 18 cm. The mid-points of its sides are joined to from another triangle whose mind-points, in turn, are joined to from still another triangle. the process is continued indefinitely. Find the sum of the (i) Perimeters of all the triangles. (ii) Areas of all triangles.
View full solution
If one A.M., A and two geometric means G1 and G2 inserted between any two positive number, show that $\frac{\text{G}^2_1}{\text{G}_2}+\frac{\text{G}^2_2}{\text{G}_1}=2\text{A}.$
View full solution

Generate a Geometric Progressions paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App