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# Algebra

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Find the sum of the first six terms in the geometric sequence 1/2, 1/8, 1/16, .... Express your answer as a common fraction.

Jun 12, 2021

#1
+524
+2

I think you missed a term, the GP should be : 1/2, 1/4, 1/8, 1/16,...

⇒ a = 1/2

r = 1/2

n = 6

$${S}_{n}={a(1-r^n)\over 1-r}$$

$$= {{1\over 2}(1- {1\over 2^6})\over {1- {1\over 2}}}$$

$$=1- {1\over 2^6}$$

$$={63 \over 64}$$

$${S}_{6}= {63\over 64}$$

Jun 12, 2021

#1
+524
+2

I think you missed a term, the GP should be : 1/2, 1/4, 1/8, 1/16,...

⇒ a = 1/2

r = 1/2

n = 6

$${S}_{n}={a(1-r^n)\over 1-r}$$

$$= {{1\over 2}(1- {1\over 2^6})\over {1- {1\over 2}}}$$

$$=1- {1\over 2^6}$$

$$={63 \over 64}$$

$${S}_{6}= {63\over 64}$$

amygdaleon305 Jun 12, 2021