Given the geometric series 256+p+64-32+
Determine the value of p
T2/T1 = T3/T2
P/256 = 64/P
Then you cross multiply
P squared = 16 384
Put square root on both sides
P = -128
Note that the answer of the square root has +/-
Actually the -32 tells us p = -128 with a common ratio of -1/2
64/p = -32/64
-32p = 4096
p = -128
To determine the value of p, we can analyze the given geometric series. A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
The given series is:
256 + p + 64 - 32 + ...
We can see that the common ratio between consecutive terms is -2 because each term is obtained by multiplying the previous term by -2.
Now, let's break down the series and express it in a simplified form:
256 + p + 64 - 32 + ...
The first term is 256.
The second term is obtained by multiplying the first term by the common ratio (-2):
p = 256 * (-2) = -512
The third term is obtained by multiplying the second term by the common ratio (-2):
64 = -512 * (-2) = 1024
The fourth term is obtained by multiplying the third term by the common ratio (-2):
-32 = 1024 * (-2) = -2048
So, the simplified form of the series becomes:
256 + (-512) + 1024 + (-2048) + ...
To find the value of p, we sum up the terms in the series:
p = 256 + (-512) + 1024 + (-2048) + ...
Using the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum of the series, a is the first term, and r is the common ratio.
Plugging in the values, we have:
p = 256 / (1 - (-2))
p = 256 / 3
p = 85.333...
Therefore, the value of p in the geometric series is approximately 85.333.
128
Obviously the common ratio
r = 1 / 2 = 0.5
256 ∙ 0.5 = 128
128 ∙ 0.5 = 64
64∙ 0.5 = 32