Maths-

General

Easy

Question

# Fifth term of G.P is 2 The product of its first nine terms is

- 1024
- 256
- 512
- 356

Hint:

### Given is only the fifth term of the G.P. and asked to find the product of 9 terms. We will consider the first term as a and the r be the common ratio of the whole G.P. then we can simply equate the fifth term as . Then remaining 9 terms will be multiplied such that their product will be in the form of

and we will try to adjust this in the form of fifth term. So let’s solve it!

## The correct answer is: 512

### Detailed Solution

Given that

term of a G.P. is 2

Let first term as a and the r be the common ratio of the whole G.P.

Then fifth term will be

But we are asked to find the product of 9 terms of the G.P.

So we can write the product as

So ,

Now we can write the terms with base a separately and those with r separately.
Now adding the powers of the bases separately,
But we have to write this in the form of power 4,
Now we will take the common power out,
Putting the value of fifth term in above bracket,
Thus, the product of its first nine terms is 512.

Here note that the fifth term is having fourth power of 2 and not fifth power. We need not to find all nine terms separately; only finding the product is enough because that product will then be written in the form of the term that is known. Terms in a G.P. are having a common ratio in between. That’s why the power of r is increasing as the terms are increasing.

### Related Questions to study

Maths-

### If a, b, c are in A.P then , are in

### If a, b, c are in A.P then , are in

Maths-General

biology

### The ultimate source of organic evolution is

### The ultimate source of organic evolution is

biologyGeneral

Maths-

### If are in A.P with common difference then sind terms]

### If are in A.P with common difference then sind terms]

Maths-General

Maths-

### The sum of all integers between 50 and 500 which are divisible by 7 is

### The sum of all integers between 50 and 500 which are divisible by 7 is

Maths-General

Maths-

### digits )=

### digits )=

Maths-General

maths-

### In a as shown in figure given that , then the value of is

### In a as shown in figure given that , then the value of is

maths-General

physics-

### A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies

### A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies

physics-General

physics-

### A particle of mass attracted with a string of length is just revolving on the vertical circle without slacking of the string. If and are speed at position and then

### A particle of mass attracted with a string of length is just revolving on the vertical circle without slacking of the string. If and are speed at position and then

physics-General

physics-

### A bob of mass is suspended by a massless string of length . The horizontal velocity at position is just sufficient to make it reach the point . The angle at which the speed of the bob is half of that at , satisfies

### A bob of mass is suspended by a massless string of length . The horizontal velocity at position is just sufficient to make it reach the point . The angle at which the speed of the bob is half of that at , satisfies

physics-General

physics-

### A body of mass is moving with a uniform speed along a circle of radius , what is the average acceleration in going from to ?

### A body of mass is moving with a uniform speed along a circle of radius , what is the average acceleration in going from to ?

physics-General

Physics-

### Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

### Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

Physics-General

physics-

### A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by

### A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by

physics-General

physics-

### In a two dimensional motion of a particle, the particle moves from point , position vector . If the magnitudes of these vectors are respectively, =3 and and the angles they make with the -axis are and 15, respectively, then find the magnitude of the displacement vector

### In a two dimensional motion of a particle, the particle moves from point , position vector . If the magnitudes of these vectors are respectively, =3 and and the angles they make with the -axis are and 15, respectively, then find the magnitude of the displacement vector

physics-General

Physics-

### A particle is moving on a circular path of radius with uniform velocity . The change in velocity when the particle moves from tois

### A particle is moving on a circular path of radius with uniform velocity . The change in velocity when the particle moves from tois

Physics-General

Physics-

### From an inclined plane two particles are projected with same speed at same angle , one up and other down the plane as shown in figure, which of the following statements is/are correct?

### From an inclined plane two particles are projected with same speed at same angle , one up and other down the plane as shown in figure, which of the following statements is/are correct?

Physics-General