Geometric progression Questions

The third term of a GP is 3. What is the product of its first five terms??

Consider the following statements:

(1) If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.

(2) If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.

Which of the above statements is/are correct?

If p^x = q^y = rz, where x, y and z are in GP, then consider the following statements:

I. p, q and r are in AP.

II. ln p, ln q and ln r are in GP.

Which of the statements given above is/are correct?

The sum of the first 8 terms of a GP is 5 times the sum of its first 4 terms. If r ≠ 1 is the common ratio, then what is the number of possible real values of k?

Let x > 1, y > 1 and z > 1 be in GP. Then

 1/*1+ lnx, 1/1+ lny and 1/1+ lnz  are

 If G is the geometric mean of numbers

1, 2, 2², 2³, ..., 2ⁿ⁻¹,

then what is the value of

1 + 2log₂G ?

 If

then which one of the following is correct?

If x, y, z are in GP, then which of the following is/are correct?

(1) ln(3x), ln(3y), ln(3z) are in AP

(2) xyz + ln(x), xyz + ln(y), xyz + ln(z) are in HP

Select the correct answer using the code given below: