How to find the sum of the first 7 terms of the geometric sequence: 24, 12, 6, 3, ..... ?

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How to find the sum of the first 7 terms of the geometric sequence: 24, 12, 6, 3, ..... ?

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Answer 1 · 2018-07-03T07:31:23

See explanation below

Explanation:

In a geometric sequence, the sum of $n$ $n$ terms is given by

$S_{n} = a_{1} \frac{r^{n} - 1}{r - 1}$ $S_n=a_1(r^n-1)/(r-1)$

In our case we need to find the ratio. Obviously $r = \frac{1}{2}$ $r=1/2$ and $a_{1} = 24$ $a_1=24$ , then applying formula

$S_{7} = 24 \frac{{(\frac{1}{2})}^{7} - 1}{\frac{1}{2} - 1} = 47.625$ $S_7=24((1/2)^7-1)/(1/2-1)=47.625$

Answer 2 · 2018-07-03T07:43:50

$S_{7} = \frac{381}{8}$ $S_7=381/8$

Explanation:

$the sum to n terms of a geometric sequence is$ $"the sum to n terms of a geometric sequence is"$

$∙ x S_{n} = \frac{a (1 - r^{n})}{1 - r}$ $•color(white)(x)S_n=(a(1-r^n))/(1-r)$

$where a is the first term and r the common ratio$ $"where a is the first term and r the common ratio"$

$•color(white)(x)r=a_2/a_1=a_3/a_2=......=a_n/a_(n-1)$

$"here "a=24$

$"and "r=12/24=6/12=3/6=1/2$

$S_7=(24(1-(1/2)^7))/(1-1/2)$

$color(white)(xx)=(24(1-1/128))/(1/2)$

$color(white)(xx)=(24xx127/128)/(1/2)$

$color(white)(xx)=48xx127/128=6096/128=381/8$

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How to find the sum of the first 7 terms of the geometric sequence: 24, 12, 6, 3, ..... ?

2 Answers

Explanation:

Explanation:

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