Question

If the numbers 1/4, x, 4 are three consecutive terms of a G.P. Find the value of x​

Answer 1

Given :  numbers 1/4, x, 4 are three consecutive terms of a G.P.

To Find :  the value of x​

Solution:

if a , b and c are  three consecutive terms of a G.P.

=> b² = ac

1/4, x, 4 are three consecutive terms of a G.P.

=> x² = (1/4)(4)

=> x² = 1

=> x = ± 1

Hence two possible values of x are

1 and  - 1

GP

1/4    1     4     16  and so on

GP with common ratio   4

1/4  -1     4   -16  and so on

GP with common ratio   -4

Learn More:

In an infinite g.P. Each term is equal to three times the sum of all the ...

brainly.in/question/9079152

In an infinite gp series the first term is p and infinite sum is s then p ...

brainly.in/question/12999165

Answer 2

Step-by-step explanation:

Given: If the numbers 1/4, x, 4 are three consecutive terms of a G.P.

To find: Find the value of x.

Solution:

We know that common ratio is same.

Step 1: Find common ratio of first two numbers

$r = \frac{x}{ \frac{1}{4} } \\ \\ r = 4x ...eq1$

Step 2: Find common ratio of last two numbers

$r = \frac{4}{x} ...eq2$

Step 3: Equate both

$4x = \frac{4}{x}$

${x}^{2} = 1 \\ \\ x = ±1$

Final answer:

x=±1

Hope it helps you.

To learn more on brainly:

If (a-2), 8,16, are in Gp then a =

https://brainly.in/question/45885832

If x > 0 then find :

$\sum^{ \infty}_{x = 1} \left( \dfrac{x}{x + 1} \right)^{n - 1}$

https://brainly.in/question/45859172