# Selecting Consecutive Terms in GP

## Trending Questions

**Q.**

Find three numbers in G.P. whose sum is 38 and their product is 1728.

**Q.**

The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

**Q.**

The sum of first three terms of a G.P. is 1312 and their product is - 1. Find the G.P.

**Q.**

The sum of first two terms of a G.P is $1$ and every term of this series is twice of its previous term, then the first term will be

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{3}{4}$

**Q.**

Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.

**Q.**

The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is 8712. Find them.

**Q.**In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is

- 8
- 4
- 24
- 16

**Q.**

The value of p and qp≠0, q≠0 for which p, q are the roots of the equation: x2+px+q=0 are

p = 1, q = 2

p = -1, q =2

p = 1, q = -2

p = -1, q = -2

**Q.**

Find three numbers in G.P. whose sum is 65 and whose product is 3375.

**Q.**

If a and b are the roots of x2−3x+p=0 and c, d are the roots x2−12x+q=0, Where a, b, c, d form a G.P. Prove that (q + p) : (q - p) = 17 : 15.

**Q.**

If (a - b), (b - c), (c - a) are in G.P. then prove that (a+b+c)2=3(ab+bc+ca)

**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.**

If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x < -1 or x > 3.

**Q.**

The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.

**Q.**If f(x+y)=f(x)f(y) and ∞∑x=1f(x)=2, x, y ∈ N, where N is the set of all natural numbers, then the value of f(4)f(2) is:

- 23
- 19
- 13
- 49

**Q.**Three numbers form a G.P. If the 3rd term is decreased by 64, then the three numbers thus obtained will constitute an A.P. If the second term of this A.P. is decreased by 8, a G.P. will be formed again, then the numbers will be

- 4, 20, 36
- 4, 12, 36
- 4, 20, 100
- None of the above

**Q.**

If $a,4,b$are in $AP$ and $a,2,b$are in $GP$ then $\frac{1}{a},1,\frac{1}{b}$ are in

$AP$

$GP$

$HP$

none of these

**Q.**Let a, b, c be three distinct real numbers in geometric progression. If x is real and a+b+c=xb, then x can be

- −2
- 3
- −1
- 4

**Q.**

If a, b, c are in G.P. then prove that : a2+ab+b2bc+ca+ab=b+ac+b

**Q.**If the 10th term of a GP is 9 and 4th term is 4, then its 7th term is

**Q.**If three distinct real numbers a, b, c are in G.P and a+b+c=ax, then

- x ∊ (-1, ∞)
- none of these

**Q.**Given the geometric progression 3, 6, 12, 24, .... The term 12288 would occur as the

- 11thterm
- 12thterm
- 13thterm
- 14thterm

**Q.**

The product of three numbers in $G.P.$ is $216.$ If $2,8,6$ be added to them$,$ the results are in $A.P.$ Find the numbers$.$

**Q.**Sum of 13, 115, 135, 163, ……2n terms is

- 2n4n+1
- 1n+1
- 12n+1
- 12n−1

**Q.**

Find the sum of the GP (1+x)21+(1+x)22+......(1+x)30

**Q.**If the geometric sequences 162, 54, 18, .... and 281, 227, 29, .... have their nth term equal, find the value of n

**Q.**If 5p2−7p−3=0 and 5q2−7q−3=0, p≠q, then the equation whose roots are 5p−4q and 5q−4p is :

- 5x2+x−439=0
- 5x2+7x−439=0
- 5x2−7x−439=0
- 5x2+7x+439=0

**Q.**Let a, b, c be three distinct real numbers in geometric progression. If x is real and a+b+c=xb, then x can be

- −2
- −1
- 3
- 2

**Q.**If the product of three consecutive term in G.P is 216 and sum of their products in pairs is 156, find them.

**Q.**If x, G1, G2, y be the consecutive terms of a G.P., then the value of G1 G2 will be

- yx
- xy
- xy
- √xy