Common Ratio

Q. The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is

1. $\frac{\sqrt{5}-1}{2}.$
2. $\frac{1-\sqrt{5}}{2}.$
3. $2\sqrt{5}$
4. 1

Q. If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is
[Roorkee 1972]

1. $-\frac{3}{2}$
2. $\frac{3}{2}$
3. 2
4. 3

Q.

If a, b, c are in G.P, then

1. a(b² + c²) = c(b² + c²)
2. a(b² + c²) = c(a² + b²)
3. a²(b + c) = c²(a + b)
4. none of these

Q. Three positive numbers form an increasing G.P. If the middle term in this G.P is doubled, then new numbers are in A.P. Then, the common ratio of the G.P. is

1. $\sqrt{2}+\sqrt{3}$
2. $3+\sqrt{2}$
3. $2-\sqrt{3}$
4. $2+\sqrt{3}$

Q. If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is

1. $1$
2. $\frac{4}{3}$
3. $\frac{8}{5}$
4. $\frac{7}{4}$

Q. If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

1. 3
2. $\frac{1}{3}$
3. 2
4. $\frac{1}{2}$

Q. A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Q. The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Q.

In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is

1. $-\frac{4}{5}$

2. $\frac{1}{5}$

3. none of these

4. 4

Q.

If $\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x\ne 0),$ then show that a, b, c and d are in G.P.