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If sum of n term of GP with last term 128 and r =2 is 255 then value of n is?
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If sum of n term of GP with last term 128 and r =2 is 255 then value o...
Calculating the number of terms in a Geometric Progression (GP)
- To find the number of terms (n) in a Geometric Progression (GP), we can use the formula for the sum of n terms in a GP.
Given values:
- Last term (a_n) = 128
- Common ratio (r) = 2
- Sum of n terms (S_n) = 255
Formula:
- S_n = a * (r^n - 1) / (r - 1)
Substitute the given values into the formula:
- 255 = 128 * (2^n - 1) / (2 - 1)
Simplify the equation:
- 255 = 128 * (2^n - 1)
- 255 = 128 * 2^n - 128
Now, solve for n:
- 255 = 128 * 2^n - 128
- 255 + 128 = 128 * 2^n
- 383 = 128 * 2^n
- 2^n = 383 / 128
- 2^n = 2^2.99
Since 2^n = 2^3, n = 3
Therefore, the number of terms in the Geometric Progression is 3.
- To find the number of terms (n) in a Geometric Progression (GP), we can use the formula for the sum of n terms in a GP.
Given values:
- Last term (a_n) = 128
- Common ratio (r) = 2
- Sum of n terms (S_n) = 255
Formula:
- S_n = a * (r^n - 1) / (r - 1)
Substitute the given values into the formula:
- 255 = 128 * (2^n - 1) / (2 - 1)
Simplify the equation:
- 255 = 128 * (2^n - 1)
- 255 = 128 * 2^n - 128
Now, solve for n:
- 255 = 128 * 2^n - 128
- 255 + 128 = 128 * 2^n
- 383 = 128 * 2^n
- 2^n = 383 / 128
- 2^n = 2^2.99
Since 2^n = 2^3, n = 3
Therefore, the number of terms in the Geometric Progression is 3.
Community Answer
If sum of n term of GP with last term 128 and r =2 is 255 then value o...
n=8
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If sum of n term of GP with last term 128 and r =2 is 255 then value of n is?
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If sum of n term of GP with last term 128 and r =2 is 255 then value of n is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If sum of n term of GP with last term 128 and r =2 is 255 then value of n is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of n term of GP with last term 128 and r =2 is 255 then value of n is?.
If sum of n term of GP with last term 128 and r =2 is 255 then value of n is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If sum of n term of GP with last term 128 and r =2 is 255 then value of n is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of n term of GP with last term 128 and r =2 is 255 then value of n is?.
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