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Which term of the following sequence is 64?
2 , 2√2, 4, .....
- a)12
- b)10
- c)11
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which term of the following sequence is 64?2 , 2√2, 4, .....a)12...
Given sequence : 2, 2√2, 4….
First term a1 = a = 2 and 2nd term a2 = 2√2, then
Common ratio r = a2/a = (2√2)/2
Let an = 64
∴ ar(n-1) = 64
⇒ 2.(√2)(n-1) = 32
⇒ (2)(n-1)/2 = 32
∴ (2)(n-1)/2 = (2)5
⇒ (n − 1)/2 = 5,
⇒ n = 11
First term a1 = a = 2 and 2nd term a2 = 2√2, then
Common ratio r = a2/a = (2√2)/2
Let an = 64
∴ ar(n-1) = 64
⇒ 2.(√2)(n-1) = 32
⇒ (2)(n-1)/2 = 32
∴ (2)(n-1)/2 = (2)5
⇒ (n − 1)/2 = 5,
⇒ n = 11
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Which term of the following sequence is 64?2 , 2√2, 4, .....a)12...
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Which term of the following sequence is 64?2 , 2√2, 4, .....a)12...
The given sequence is 2, 22, 4, ...
To find the term that is equal to 64, we need to determine the pattern or rule followed by the sequence.
1. Identifying the pattern:
- The first term is 2.
- The second term is obtained by squaring the first term and subtracting 2: 2^2 - 2 = 2.
- The third term is obtained by subtracting 2 from the second term: 2 - 2 = 0.
- The fourth term is obtained by squaring the third term and subtracting 2: 0^2 - 2 = -2.
- The fifth term would be obtained by subtracting 2 from the fourth term: -2 - 2 = -4.
- The sixth term would be obtained by squaring the fifth term and subtracting 2: (-4)^2 - 2 = 14.
- Continuing this pattern, the seventh term would be obtained by subtracting 2 from the sixth term: 14 - 2 = 12.
- The eighth term would be obtained by squaring the seventh term and subtracting 2: 12^2 - 2 = 142.
- The ninth term would be obtained by subtracting 2 from the eighth term: 142 - 2 = 140.
- The tenth term would be obtained by squaring the ninth term and subtracting 2: 140^2 - 2 = 19598.
- The eleventh term would be obtained by subtracting 2 from the tenth term: 19598 - 2 = 19596.
2. Finding the term that is equal to 64:
By observing the pattern, we can see that the terms alternate between squaring the previous term and subtracting 2 from the previous term.
To find the term that is equal to 64, we need to determine the position of the term. Starting from the first term, we can see that the pattern repeats every two terms.
Since 64 is a multiple of 2, we need to find the position of 64 in the sequence.
By counting the terms, we can determine that the 11th term is equal to 64.
Thus, the correct answer is option C) 11.
To find the term that is equal to 64, we need to determine the pattern or rule followed by the sequence.
1. Identifying the pattern:
- The first term is 2.
- The second term is obtained by squaring the first term and subtracting 2: 2^2 - 2 = 2.
- The third term is obtained by subtracting 2 from the second term: 2 - 2 = 0.
- The fourth term is obtained by squaring the third term and subtracting 2: 0^2 - 2 = -2.
- The fifth term would be obtained by subtracting 2 from the fourth term: -2 - 2 = -4.
- The sixth term would be obtained by squaring the fifth term and subtracting 2: (-4)^2 - 2 = 14.
- Continuing this pattern, the seventh term would be obtained by subtracting 2 from the sixth term: 14 - 2 = 12.
- The eighth term would be obtained by squaring the seventh term and subtracting 2: 12^2 - 2 = 142.
- The ninth term would be obtained by subtracting 2 from the eighth term: 142 - 2 = 140.
- The tenth term would be obtained by squaring the ninth term and subtracting 2: 140^2 - 2 = 19598.
- The eleventh term would be obtained by subtracting 2 from the tenth term: 19598 - 2 = 19596.
2. Finding the term that is equal to 64:
By observing the pattern, we can see that the terms alternate between squaring the previous term and subtracting 2 from the previous term.
To find the term that is equal to 64, we need to determine the position of the term. Starting from the first term, we can see that the pattern repeats every two terms.
Since 64 is a multiple of 2, we need to find the position of 64 in the sequence.
By counting the terms, we can determine that the 11th term is equal to 64.
Thus, the correct answer is option C) 11.
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Which term of the following sequence is 64?2 , 2√2, 4, .....a)12b)10c)11d)8Correct answer is option 'C'. Can you explain this answer?
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