Geometric Progression

Q.

If the first term and common ratio of a G.P. are 5 and -5 respectively, then the ___ term is 3125.

1. $6^{\text{th}}$

2. $5^{\text{th}}$

3. $8^{\text{th}}$

4. $7^{\text{th}}$

Q.

Find the number of terms in the G.P 6, 12, 24 ... 1536.

1. 8

2. 10

3. 9

4. 6

Q. The next term of the sequence $1,2,4,8,16$ is .

1. 128
2. 32
3. 64

Q.

How many positive integers between $1000$ and $9999$ inclusive are not divisible by $3$?

Q.

How many positive integers between $1000$ and $9999$ inclusive are even?

Q.

How many positive integers between $1000$ and $9999$ inclusive are divisible by $5$ and $7$?

Q.

Show that the progressions are GP. Also, find the common ratio.

$4,-2,1,-1/2,\dots$

Q. The sum of all natural numbers less than 200, that are divisible by 3 or by 5, is

Q.

Find the number of terms in the G.P 6, 12, 24 ... 1536.

1. 8

2. 10

3. 9

4. 6

Q.

The sequence 4, 8, 16, 32, ... is a G.P.

1. True

2. False

Q.

The $4^{\mathrm{th}}$ term of a GP is $16$and $7^{\mathrm{th}}$ term is $128$ .Find the first term and common ratio of the series.

Q. Find $a_{20}$ of a geometric sequence if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

1. ${20}^{20}$
2. $\frac{1}{{20}^{20}}$
3. $\frac{1}{20}$
4. $\frac{1}{{20}^{19}}$

Q.

What is the sum of the first 25 terms of the A.P -10, -7, -4, .......?

1. 580

2. 620

3. 650

4. 560

Q.

If the $\mathrm{nth}$ term of an AP is $(2\mathrm{n}+1)$, then find the sum of the first $\mathrm{n}$ terms of the AP.

Q.

If the first term of a G.P. is 1 and the sum of the third and fifth term is 20, find its common ratio.

1. 2

2. -2

3. 5

4. -5

Q.

If a, b, c are in A.P. then $3^a$, $3^b$, $3^c$ are in ___.

1. G.P.

2. H.P.

3. None of these

4. A.P.

Q. Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

Q.

If the numbers $5,x,125$ are in G.P. what is the value of $x$?

1. 25

2. 50

3. 15

4. 55

Q. What must be added to each of the numbers 1, 10, 46 so that the resulting numbers are in G.P.?

1. 2

Q. If the equation $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots equal in magnitude ut opposite in sign, then m =

Q.

If the $(p+q{)}^{th}$ term of a G.P. is m and $(p-q{)}^{th}$ term is n, then pth term will be _____.

1. $\left(\frac{m}{n}\right)$

2. $(m-n)$

3. $mn$

4. $\sqrt{mn}$

Q. The sequence N of natural numbers is divided into classes as follows
$1$
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
.......................................................
......................................................................
Find the sum of the numbers of n-th row

1. $3n^3+4n^2+4n$
2. $3n^3-4n^2+4n$
3. $\frac{3n^3-4n^2-4n}{2}$
4. $\frac{3n^3-4n^2+4n}{2}$

Q. If the $3^{\text{rd}}$ term of a G.P is 4, then the product of its first five terms is .

1. 512
2. 1024
3. 128

Q.

What is the condition for geometric progression?

Q. If $x,y$ and $z$ are three consecutive terms of a G.P such that $xyz=8,$ then $y$ equals ____.

1. 2
2. 32
3. 8
4. 7

Q. The sum of three numbers in $G.P.$ is $14$. If the first two terms are each increased by $1$ and the third term decreased by $1$, the resulting numbers are in $A.P.$ Find the numbers.

Q. Let $\alpha ,\beta$ be the roots of $x^2-x+p=0and\gamma ,\delta$ be the roots of $x^2-4x+q=0.$~If $\alpha ,\beta ,\gamma ,\delta ,$ are in G.P., then the integral values of p and q respectively, are

1. -2, -32
2. -2, 3
3. -6, -32
4. -6, 3

Q.

Question 32

In the following question, out of the four options, only one is correct. Write the correct answer.

Cube of $-\frac{1}{2}$ is

(a) $\frac{1}{8}$

(b) $\frac{1}{16}$

(c) $-\frac{1}{8}$

(d) $-\frac{1}{16}$

Q. If a, b, c are in GP, then the equations $a{x}^2+2bx+c=0$ and $d{x}^2+2ex+f=0$ have a common root, if $\frac{d}{a},\frac{e}{b},\frac{f}{c}$ are in

1. AP
2. GP
3. HP
4. None of these

Q.

Which of the following is not a geometric progression?

1. 3, 6, 12, 24

2. 3, 3, 3, 3

3. 3, 9, 27, 81

4. 3, 6, 9, 12