Pregunta
Find the partial sum \( S_{8} \) for the geometric sequence with \( a=2, r=2 \). \( S_{8}= \) Question Help: \( \square \) Video Submit Question
Ask by Barnett Vaughan. in the United States
Feb 14,2025
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The partial sum \( S_{8} \) is 510.
Solución
To find the sum of the first 8 terms of a geometric sequence with a = 2 and r = 2, use the formula:
Sₙ = a( rⁿ – 1 ) / (r – 1)
For n = 8:
S₈ = 2(2⁸ – 1) / (2 – 1)
S₈ = 2(256 – 1) / 1
S₈ = 2(255)
S₈ = 510
Thus, the partial sum S₈ is 510.
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Simplifique esta solución Beyond the Answer
The formula for the partial sum \( S_n \) of a geometric sequence is given by: \[ S_n = a \frac{1 - r^n}{1 - r} \] For your sequence where \( a = 2 \) and \( r = 2 \), we want to find \( S_8 \). Plugging in the values, we get: \[ S_8 = 2 \frac{1 - 2^8}{1 - 2} = 2 \frac{1 - 256}{-1} = 2 \cdot 255 = 510 \] So, \( S_{8} = 510 \).
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