Question

Given that the positive numbers p,q,r,s are in G.P. , which of the following must be true?
A. kp, kq,kr,ks are in G.P. where k is a non-zero constant.
B. a^p , a^q, a^r, a^s are in G.P. where a is a positive constant.
C. logp, logq, logr, logs are in A.P.

Answer 1

@ganeshie8

Answer 2

well, A ofcuz

Answer 3

why?

Answer 4

what does G.P mean?

Answer 5

common ratio..

Answer 6

how about AP?

Answer 7

@Loser66 , GP is Geometric Progression or 几何级数 in Chinese, AP is Arithmetic Progression or 算数级数 in CHinese. LOL

Answer 8

I am not chinese, lol

Answer 9

I'm ofcuz

Answer 10

I agree with caozeyuan, it's a

Answer 11

logic is: if p,q,r,s in GP, let d is common ratio,
then kp, kq,kr,ks is in another GP whose common ratio is kd

Answer 12

@caozeyuan oh, you know chinese XD??
@Loser66 I know the definition, but i don't know why B and C are not

Answer 13

for choice c:

write p, q, r, s as
p, kp, k^2 p , k^3 p

take the log:
log(p), log(kp), log(k^2 p), log(k^3 p)
log(p) , log(k) + log(p), log(k^2)+ log(p), log(k^3)+ log(p)
or
log(p) , log(p) + log(k), log(p) + 2 log(k), log(p) + 3 log(k)

Answer 14

@phi, that means the different is not a constant; contradict to definition of AP, right?

Answer 15

for choice c, you get a common difference of log(k), so you have an arithmetic progression

Answer 16

oh, got you

Answer 17

ohh..

Answer 18

for choice b

write p, q, r, s as
p, kp, k^2 p , k^3 p


look at the ratios of two successive terms:
a^q / a^p = a^(q-p) = a^(kp-p)= a^(p(k-1))

we need to find the same ratio for
a^r/a^q = a^(r-q)= a^(k^2 p - k p)
those ratios are different
so not a G.P.

Answer 19

for A (just to be complete)

kq/kp = q/p
kr/kq = r/q

using
write p, q, r, s as
p, kp, k^2 p , k^3 p

q/p is kp/p = k

r/q is k^2 p/ kp = k
and so on...

Answer 20

ohh, clear, that means A and C are correct?