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How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?
- a)9
- b)7
- c)8
- d)6
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
How many terms of the G.P. 4 + 16 + 64 + … will make the sum 546...
Sum (Sn) = a x (rn -1)/(r-1)
5460 = 4 x (4n -1)/3
16380 = 4n+1 - 4
5460 = 4 x (4n -1)/3
16380 = 4n+1 - 4
16384 = 4n+1
47 = 4n+1
7 = n + 1
n = 6
Most Upvoted Answer
How many terms of the G.P. 4 + 16 + 64 + … will make the sum 546...
Formula for the sum GP is a(r power n - 1) by r - 1 here the sum is 5460 . a=4 r=16 by 4 = 4 we need to find n. here n is no.of terms 4(4 power n - 1) by 3 = 5460 4(4 power n - 1) = 16380 4 power n - 1= 4095 4 power n=4096 4 power n = 4 power 6.[since 4096 can be written as 4 power 6] therefore n=6
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How many terms of the G.P. 4 + 16 + 64 + … will make the sum 546...
In order to determine how many terms are in the geometric progression (G.P.) 4, 16, 64, we need to identify the common ratio. We can find this by dividing any term in the sequence by its previous term.
For example, dividing 16 by 4 gives us a quotient of 4. Similarly, dividing 64 by 16 also gives us a quotient of 4. Since the common ratio is 4, we can continue this pattern to find subsequent terms in the sequence.
The next term in the G.P. would be 64 * 4 = 256, and the term after that would be 256 * 4 = 1024, and so on.
Therefore, the G.P. 4, 16, 64 has an infinite number of terms since we can continue multiplying the last term by 4 to find the next term indefinitely.
For example, dividing 16 by 4 gives us a quotient of 4. Similarly, dividing 64 by 16 also gives us a quotient of 4. Since the common ratio is 4, we can continue this pattern to find subsequent terms in the sequence.
The next term in the G.P. would be 64 * 4 = 256, and the term after that would be 256 * 4 = 1024, and so on.
Therefore, the G.P. 4, 16, 64 has an infinite number of terms since we can continue multiplying the last term by 4 to find the next term indefinitely.
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How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer?
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How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer?.
How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many terms of the G.P. 4 + 16 + 64 + … will make the sum 5460?a)9b)7c)8d)6Correct answer is option 'D'. Can you explain this answer?.
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