Question

the sum of n term of GP, whose first term 1 and the common ratio is 1/2 is equal to 1 127/128 the value of n is​

Answer 1

Answer:

n=8 is the answer

Step-by-step explanation:

Thank you

Answer 2

The value of n is 8.

Step-by-step explanation:

Since we have given that

a = 1

r = common ratio = $\dfrac{1}{2}$

Sum of n terms  = $S_n=\dfrac{1127}{128}$

Since they are in GP, so we get that

$S_n=\dfrac{a(1-r^n)}{1-r}\\\\1\dfrac{127}{128}=\dfrac{(1-0.5^n)}{1-0.5}\\\\\dfrac{255}{128}=\dfrac{1-0.5^n}{0.5}\\\\\dfrac{255\times 0.5}{128}=1-0.5^n\\\\\dfrac{1127}{128\times 2}=1-0.5^n\\\\\dfrac{255}{256}=1-0.5^n\\\\\dfrac{255}{256}-1=-0.5^n\\\\\dfrac{255-256}{256}=-0.5^n\\\\\dfrac{-1}{256}=-0.5^n\\\\n=8$

Hence, the value of n is 8.

# learn more:

The nth term of GP is 128 and the sum of n terms is 255. If it's common ratio is 2. Find the first term?

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