To find the number of terms needed to obtain a total of 127.5, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r), where S is the desired sum, a is the first term, and r is the common ratio.
In this case, we want the sum to be 127.5, the first term is 64, and the common ratio is 1/2:
127.5 = 64 / (1 - 1/2)
Simplifying the equation:
127.5 = 64 / (1/2)
127.5 = 64 * 2
127.5 = 128
Since the sum is equal to 128, we don't need to add any terms to obtain a total of 127.5.
the first term of gp is 64 & the common ratio is half . how many terms must be added to obtain a total of 127 and a half
5 answers
what a load of rubbish.
The sequence goes 64, 32, 16, ... + 1
To find how many terms sum to 127, solve
64(1 - 1/2^n)/(1 - 1/2) = 127
n = 7
But then, we already knew that, since 64=2^6
The sequence goes 64, 32, 16, ... + 1
To find how many terms sum to 127, solve
64(1 - 1/2^n)/(1 - 1/2) = 127
n = 7
But then, we already knew that, since 64=2^6
Apologies for the incorrect response. You are absolutely right.
To find the number of terms needed to obtain a total of 127.5, we can solve the equation:
64(1 - (1/2)^n) / (1 - 1/2) = 127.5
Simplifying the equation:
64(1 - (1/2)^n) = 255
1 - (1/2)^n = 255/64
(1/2)^n = 1 - 255/64
(1/2)^n = 9/64
To simplify the equation, we can express 9/64 as (3/8)^2:
(1/2)^n = (3/8)^2
Taking the logarithm of both sides:
n log(1/2) = 2 log(3/8)
n = 2 log(3/8) / log(1/2)
n ≈ 2 * (-0.415) / (-0.301)
n ≈ 2.486
Since n represents the number of terms in the sequence, we need to round up to the nearest whole number. Therefore, we need to add 3 terms in order to obtain a total of 127.5.
To find the number of terms needed to obtain a total of 127.5, we can solve the equation:
64(1 - (1/2)^n) / (1 - 1/2) = 127.5
Simplifying the equation:
64(1 - (1/2)^n) = 255
1 - (1/2)^n = 255/64
(1/2)^n = 1 - 255/64
(1/2)^n = 9/64
To simplify the equation, we can express 9/64 as (3/8)^2:
(1/2)^n = (3/8)^2
Taking the logarithm of both sides:
n log(1/2) = 2 log(3/8)
n = 2 log(3/8) / log(1/2)
n ≈ 2 * (-0.415) / (-0.301)
n ≈ 2.486
Since n represents the number of terms in the sequence, we need to round up to the nearest whole number. Therefore, we need to add 3 terms in order to obtain a total of 127.5.
Oops. My mistake. I did not see the 127 1/2
But, it's easy, since we already know that 7 terms sum to 127, and the next term is 1/2, so 8 terms sum to 127.5
But, it's easy, since we already know that 7 terms sum to 127, and the next term is 1/2, so 8 terms sum to 127.5
No problem, thank you for pointing out the mistake. You are absolutely right. We already know that 7 terms sum to 127, and since the next term is 1/2, adding an additional term will give us the total of 127.5.
Hence, we need to add 8 terms in order to obtain a total of 127.5.
Hence, we need to add 8 terms in order to obtain a total of 127.5.