Write the GP. if a = 256, r = −1/2
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I will assume you meant to ask “What is the sum of the FIRST 15 terms?”
We will need the first term (a1a1), the common ratio (rr), and the number of terms (nn).
We will use this formula: Sn=a1(1−rn)(1−r).Sn=a1(1−rn)(1−r).
We are given a1=12a1=12 and n=15n=15. We need to find rr.
The ninth term is 128=(a1)r8=12r8128=(a1)r8=12r8. That means 256=r8256=r8, and r=2r=2.
So S15=12(1−215)1−2=12(1−32768)−1=−32767−2=16383.5S15=12(1−215)1−2=12(1−32768)−1=−32767−2=16383.5
We will need the first term (a1a1), the common ratio (rr), and the number of terms (nn).
We will use this formula: Sn=a1(1−rn)(1−r).Sn=a1(1−rn)(1−r).
We are given a1=12a1=12 and n=15n=15. We need to find rr.
The ninth term is 128=(a1)r8=12r8128=(a1)r8=12r8. That means 256=r8256=r8, and r=2r=2.
So S15=12(1−215)1−2=12(1−32768)−1=−32767−2=16383.5S15=12(1−215)1−2=12(1−32768)−1=−32767−2=16383.5
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