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If p,q,r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in
- a)Arithmetic progression
- b)Geometric progression
- c)Harmonic progression
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If p,q,r are in one geometric progression and a, b, c are in another g...
Let the common ratio be K1 for p, q and r.
q = K1p
& r = (K1)2p
Let the common ratio be K2 for a, b and c
b = K2a
& c = (K2)2a
bq = (K1K2)ap
&Cr = (K1K2)2ap
So ap, bq, cr are in GP.
q = K1p
& r = (K1)2p
Let the common ratio be K2 for a, b and c
b = K2a
& c = (K2)2a
bq = (K1K2)ap
&Cr = (K1K2)2ap
So ap, bq, cr are in GP.
Most Upvoted Answer
If p,q,r are in one geometric progression and a, b, c are in another g...
Explanation:
Given:
- p, q, r are in one geometric progression
- a, b, c are in another geometric progression
Proof:
Geometric Progression:
- In a geometric progression, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
- For a geometric progression with terms a, ar, ar^2, ar^3, ..., the common ratio is r.
Relationship:
- If ap, bq, cr are formed from the given sequences, we can see that the terms are multiplied by a common ratio.
- ap = a * p = a * (a * r) = a^2 * r
- bq = b * q = b * (b * r) = b^2 * r
- cr = c * r = c * (c * r) = c^2 * r
Conclusion:
- Since ap, bq, cr are formed by multiplying the terms of the given sequences by a common ratio (r), they are in a geometric progression.
Given:
- p, q, r are in one geometric progression
- a, b, c are in another geometric progression
Proof:
Geometric Progression:
- In a geometric progression, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
- For a geometric progression with terms a, ar, ar^2, ar^3, ..., the common ratio is r.
Relationship:
- If ap, bq, cr are formed from the given sequences, we can see that the terms are multiplied by a common ratio.
- ap = a * p = a * (a * r) = a^2 * r
- bq = b * q = b * (b * r) = b^2 * r
- cr = c * r = c * (c * r) = c^2 * r
Conclusion:
- Since ap, bq, cr are formed by multiplying the terms of the given sequences by a common ratio (r), they are in a geometric progression.
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If p,q,r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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