Question

find the sum of g.p 4,2,1,1/2.......s10
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Answer 1

Answer:

4,2,1,1/2

10,15,20,1/5

Answer 2

EXPLANATION.

sum of Gp = 4,2,1,1/2,.........s10

First term = a = 4

common ratio = r = b/a = 2/4 = 1/2

$\rm \green{ \underline{formula \: of \: sum \: \: of \: \: n \: terms \: \: of \: an \: gp}}$

$\rm \to \: s_{n} \: = \frac{a(r {}^{n} - 1)}{r - 1}$

n = 10 terms.

$\rm \to \: s_{n} \: = \frac{4( \frac{1}{2 } {}^{10} - 1) }{ \frac{1}{2} - 1 }$

$\rm \to s_{n} \: = \frac{4( \frac{1}{1024} - 1) }{ \frac{ - 1}{2} }$

$\rm \to \: s_{n} \: = \frac{4 (\frac{1 - 1024}{1024} )}{ \frac{ - 1}{2} }$

$\rm \to \: s_{n} \: = \frac{ \frac{ - 1023}{256} }{ \frac{ - 1}{2} }$

$\rm \to \: s_{n} \: = \frac{1023}{128}$