Sample QuestionsGeometric 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 :
- A
$\frac{1}{10}$
- ✓
$\frac{1}{11}$
- C
$\frac{1}{9}$
- D
$\frac{1}{20}$
Answer: B.
View full solution →If $a, b, c$ are in $A.P.$ and $x, y, z$ are in $G.P.$, then the value of $x^{b-c} y^{c-a} z^{a-b}$ is:
Answer: B.
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 :
Answer: A.
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 :
- ✓
$\frac12$
- B
$\frac{2}{3}$
- C
$\frac13$
- D
$\frac{-1}{2}.$
Answer: A.
View full solution →The nth term of a G.P. is $128$ and the sum of its $n$ terms is $225.$ If its common ratio is $2,$ then its first term is:
Answer: A.
View full solution →If $A_1, A_2$ be two $AM's$ and $G_1, G_2$ be two $GM's$ between $a$ and $b$, then find the value of $\frac{\text{A}_1+\text{A}_2}{\text{G}_1\text{G}_2}.$
View full solution →If $\text{a} = 1 + \text{b} + \text{b}_2 + \text{b}_3 + ...\text{to }\infty,$ then write b in terms of a given that |b|<1.
View full solution →If second, third and sixth term of an A.P. are consecutive terms of a G.P., write the common ratio of G.P.
If the fifth term of a G.P. is $2$, then write the product of its $9$ terms.
View full solution →If $(p + q)^{th}$ and $(p - q)^{th}$ terms of a G.P. are m and respectively, then write its pth term.
View full solution →Find the sum of the following geometric progrssions:1, 3, 9, 27, ... to 8 terms
The sum of three numbers which are consecutive terms of an A.P. is $21$.
If the second number is reduced by $1$ and the third is increased by $1$, we obtain three consecutive terms of a G.P.
Find the numbers.
View full solution →The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
How many terms of the series 2 + 6 + 18 + ... must be make the sum equal to 728₹
Find:
The $10^{th}$ term of the G.P. $\sqrt{2},\frac{1}{\sqrt{2}},\frac{1}{2\sqrt{2}},\dots$
View full solution →Find the sum of the following series:
0.6 + 0.66 + 0.666 + ... to n terms.
If $\frac{\text{a}+\text{bx}}{\text{a}-\text{bx}}=\frac{\text{b}+\text{cx}}{\text{b}-\text{cx}}=\frac{\text{c}+\text{dx}}{\text{c}-\text{dx}}(\text{x}\neq0),$ then show that a, b, c and d are in G.P.
View full solution →Which term of the G.P.:$\sqrt{3},3,3\sqrt{3},\ \dots\text{is}729?$
View full solution →If $S$ denotes the sum of an infinite G.P. and $S_1$ denotes the sum of the squares of its terms, then prove that the first terms and common ratio are respectively $\frac{2\text{SS}_1}{\text{S}^2+\text{S}_1}\text{ and }\frac{\text{S}^2-\text{S}_1}{\text{S}^2+\text{S}_1}.$
View full solution →Find the sum of the following geometric series:$\frac{3}{5}+\frac{4}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+\ ...\ \text{to 2n terms;}$
View full solution →Find the $4^{th}$ term from the end of the G.P. $\frac12,\frac16,\frac{1}{18}\frac{1}{54},\ \dots,\ \frac{1}{4374}.$
View full solution →If $p^{th}, q^{th}$ and $r^{th}$ terms of an A.P. and G.P. are both $a, b$ and $c$ respectively, show that $a^{b-c} b^{c-a} c^{a-b} = 1.$
View full solution →Find three numbers in G.P. whose sum is $38$ and their product is $1728$.
View full solution →Find sum of these numbers in G.P. is $21$ and the sum of their aquares is $189$. Find the numbers.
View full solution →Find the $4^{\text {th }}$ term of the G.P. is $27$ and the $7$ th term is $729$ , find the G.P.
View full solution →Let $a_n$ be the nth term of the G.P. of positive numbers. Let $\sum\limits_{\text{n}=1}^{100}\text{a}_{2\text{n}}=\alpha\text{ and}\sum\limits_{\text{n}=1}^{10}\text{a}_{2\text{n}-1}=\beta,$ such that $\alpha\neq\beta.$ Prove that the common ratio of the G.P. is $\frac{\alpha}{\beta}$
View full solution →If a, b, c, are in G.P., prove that:
$\frac{1}{\text{a}^2+\text{b}^2},\frac{1}{\text{b}^2+\text{c}^2},\frac{1}{\text{c}^2+\text{d}^2}\text{ are in G.P.}$
View full solution →The product of three numbers in G.P. is $125$ and the sum of their products taken in pairs is $87\frac{1}{2}.$ Find them.
View full solution →If $a, b, c$ are in G.P., prove that:
$\frac{\text{a}^2+\text{ab}+\text{b}^2}{\text{bc}+\text{ca}+\text{ab}}=\frac{\text{b}+\text{a}}{\text{c}+\text{b}}$
View full solution →If a and b are the roots of $\text{x}^2-3\text{x}+\text{p}=0$ and c, d are roots $\text{x}^2-12\text{x}+\text{q}=0,$ where a, b, c, d from a G.P. Prove that (q + p) : (q - p) = 17 : 15.
View full solution →