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Which of the following sequeces in GP will have common ratio 3,where n is an Integer?
- a)gn = 6(3n-1)
- b)gn = 3n2 + 3n
- c)gn = 2n2 + 3
- d)gn = 2n2 + 3n
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following sequeces in GP will have common ratio 3,where n...
gn = 6( 3n-1) it is a geometric expression with coefficient of constant as 3n-1.So it is GP with common ratio 3.
Most Upvoted Answer
Which of the following sequeces in GP will have common ratio 3,where n...
Explanation:
To check which sequence has a common ratio of 3, we need to substitute the value of n in each sequence and check if the ratio of consecutive terms equals 3.
Let's substitute the value of n in each sequence and calculate the ratio of consecutive terms.
a) gn = 6(3n - 1)
- Substitute n = 1: g1 = 6(3(1) - 1) = 6(3 - 1) = 6(2) = 12
- Substitute n = 2: g2 = 6(3(2) - 1) = 6(6 - 1) = 6(5) = 30
- Ratio of consecutive terms: g2/g1 = 30/12 = 5/2 ≠ 3
b) gn = 3n^2 - 3n
- Substitute n = 1: g1 = 3(1)^2 - 3(1) = 3 - 3 = 0
- Substitute n = 2: g2 = 3(2)^2 - 3(2) = 3(4) - 6 = 12 - 6 = 6
- Ratio of consecutive terms: g2/g1 = 6/0 (division by zero is undefined)
c) gn = 2n^2 - 3
- Substitute n = 1: g1 = 2(1)^2 - 3 = 2 - 3 = -1
- Substitute n = 2: g2 = 2(2)^2 - 3 = 2(4) - 3 = 8 - 3 = 5
- Ratio of consecutive terms: g2/g1 = 5/(-1) = -5 ≠ 3
d) gn = 2n^2 - 3n
- Substitute n = 1: g1 = 2(1)^2 - 3(1) = 2 - 3 = -1
- Substitute n = 2: g2 = 2(2)^2 - 3(2) = 2(4) - 6 = 8 - 6 = 2
- Ratio of consecutive terms: g2/g1 = 2/(-1) = -2 ≠ 3
Conclusion:
After evaluating the ratio of consecutive terms for each sequence, we can conclude that only option 'a' has a common ratio of 3. Therefore, the correct answer is option 'A' (gn = 6(3n - 1)).
To check which sequence has a common ratio of 3, we need to substitute the value of n in each sequence and check if the ratio of consecutive terms equals 3.
Let's substitute the value of n in each sequence and calculate the ratio of consecutive terms.
a) gn = 6(3n - 1)
- Substitute n = 1: g1 = 6(3(1) - 1) = 6(3 - 1) = 6(2) = 12
- Substitute n = 2: g2 = 6(3(2) - 1) = 6(6 - 1) = 6(5) = 30
- Ratio of consecutive terms: g2/g1 = 30/12 = 5/2 ≠ 3
b) gn = 3n^2 - 3n
- Substitute n = 1: g1 = 3(1)^2 - 3(1) = 3 - 3 = 0
- Substitute n = 2: g2 = 3(2)^2 - 3(2) = 3(4) - 6 = 12 - 6 = 6
- Ratio of consecutive terms: g2/g1 = 6/0 (division by zero is undefined)
c) gn = 2n^2 - 3
- Substitute n = 1: g1 = 2(1)^2 - 3 = 2 - 3 = -1
- Substitute n = 2: g2 = 2(2)^2 - 3 = 2(4) - 3 = 8 - 3 = 5
- Ratio of consecutive terms: g2/g1 = 5/(-1) = -5 ≠ 3
d) gn = 2n^2 - 3n
- Substitute n = 1: g1 = 2(1)^2 - 3(1) = 2 - 3 = -1
- Substitute n = 2: g2 = 2(2)^2 - 3(2) = 2(4) - 6 = 8 - 6 = 2
- Ratio of consecutive terms: g2/g1 = 2/(-1) = -2 ≠ 3
Conclusion:
After evaluating the ratio of consecutive terms for each sequence, we can conclude that only option 'a' has a common ratio of 3. Therefore, the correct answer is option 'A' (gn = 6(3n - 1)).
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Which of the following sequeces in GP will have common ratio 3,where n is an Integer?a)gn= 6(3n-1)b)gn= 3n2+ 3nc)gn= 2n2+ 3d)gn= 2n2+ 3nCorrect answer is option 'A'. Can you explain this answer?
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