Sample QuestionsGeometric Progression questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the geometric mean between
$2a$ and $8a^3$
View full solution →Find the geometric mean between: 14 and $\frac{7}{32}$
View full solution →Find the geometric mean between: $\frac{4}{9}$ and $\frac{9}{4}$
View full solution →Find the sum of G.P. $: 3, 6, 12, …… 1536.$
View full solution →The first term of a G.P. is -3 and the square of the second term is equal to its $4^{\text {th }}$ term. Find its $7^{\text {th }}$ term.
View full solution →If a, b and c are in $G.P$., prove that:
log a, log b and log c are in $A.P.$
View full solution →Find the third term from the end of the G.P.
$\frac{2}{27}, \frac{2}{9}, \frac{2}{3}, \ldots \ldots \ldots 162$
View full solution →Find the seventh term from the end of the series: $\sqrt{2}, 2,2 \sqrt{2}, \ldots \ldots, 32$
View full solution →A geometric progression has common ratio $= 3$ and last term $= 486.$ If the sum of its terms is $728;$ find its first term.
View full solution →A boy spends Rs.$10$ on first day, Rs.$20$ on second day, Rs.$40$ on third day and so on. Find how much, in all, will he spend in $12$ days?
View full solution →How many terms of the geometric progression $1 + 4 + 16 + 64 + ……..$ must be added to get sum equal to $5461?$
View full solution →Find the sum of the sequence $-\frac{1}{3}, 1,-3,9, \ldots . . . .$. upto $8$ terms.
View full solution →The first two terms of a G.P. are $125$ and $25$ respectively. Find the $5^{th}$ and the $6^{th}$ terms of the G.P.
View full solution →Which of the following is/are correct?
Statement A: If the first term and the common ratio of a G.P. are 5 and 2 respectively, then the G.P. is $5,10,20,40 \ldots$
Statement B: Three numbers $a, b, c$ are in G.P. iff $\frac{b}{a}=\frac{c}{b}$
Statement C: In G.P.
$a=1, a_3+a_5=90$ and common ratio $r= \pm 3$
- A
- B
- C
- ✓
All A, B and C are correct
Answer: D.
View full solution →Which of the following is/are correct?
Statement (A): The next term of an G.P. $\frac{1}{6}, \frac{1}{3}, \frac{2}{3}, \ldots$ is $\frac{4}{3}$
Statement (B): The nth term of this G.P. is $\frac{1}{3}(2)^{-2}$.
Statement (C): The 6th term of this G.P. is $\frac{16}{3}$
- A
- B
- C
- ✓
All A, B and C are correct
Answer: D.
View full solution →Which of the following is/are an geometric progression (G.P.)?
1. $1,-\frac{1}{2},+\frac{1}{4},-\frac{1}{8},+\ldots+\ldots$
2. $\sqrt{3}, 3 \sqrt{3}, 3,3 \sqrt{3}, \ldots$
3. $18,-12,-6, \ldots \ldots$.
Answer: A.
View full solution →Statement (A): The first and last terms of a G.P. are 3 and 96 respectively. If the common ratio is 2 ; then the number of terms of the G.P. is 6 .
Statement (B): The sum of the n terms is 186.
Which of the statement is valid?
Answer: A.
View full solution →Statement (A): The nth term of the of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$ is $\frac{5}{2^{\prime \prime}}$
Statement (B): The 20th term of the G.P. $\frac{5}{2}, \frac{5}{9}, \frac{5}{8}, \ldots$ is $\frac{5}{2^{20}}$.
Which of the statement is valid?
Answer: C.
View full solution →Assertion : The first term and the common ratio of a G.P., is 2 and 3 respectively and whose last term is 486 . Then the sum of the whose term is 728 .
Reason: The sum of the $n$ term is $\frac{l r-a}{r-1}$,
Where $l=$ last term
- ✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: A.
View full solution →Assertion : If the 4th, 10th and 16th terms of a G.P. are $x, y$ and $z$ respectively, then the $x, y, z$ are in G.P.
Reason : The last term of an G.P. is $l=a r^{n-1}$, where $l$ is the last term of an G.P.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →Assertion: The sum of first 5 terms of the list of numbers $3,6,12 \ldots$ is 93 .
Reason : The sum of first n terms of an G.P. is given by $\frac{a\left(1-r^*\right)}{(1-r)}$; if $r <1$
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →Assertion : The 4 th term of a G.P. is 16 and the 7 th term is 128 , then the first term and the common ratio of the G.P. is 2 .
Reason : The nth term of an AP is given by $a r^{n-1}$, where $a$ and $r$ are the first term and the common ratio respectively.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →