rissaunnie
  • rissaunnie
What equation will give the sum of this geometric series? 30 + 3-1 + 3-2 + 3-3 + 3-4 + ⋯ + 3-9
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
your answer is 32 i believe
anonymous
  • anonymous
could you give me a medal
Vocaloid
  • Vocaloid
it's asking for an equation, not a number let me think about this for a sec

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anonymous
  • anonymous
woops
Vocaloid
  • Vocaloid
are those supposed to be exponents? like: 3^0 + 3^(-1) + 3^(-2)...etc
rissaunnie
  • rissaunnie
yes
Vocaloid
  • Vocaloid
ok, that makes things a lot more clear now :P first step is to identify the common ratio if we rewrite the terms as fractions, we can see the pattern more clearly 3^0 + 3^(-1) + 3^(-2) ... is equal to 1 + (1/3) + (1/9)... with me so far?
rissaunnie
  • rissaunnie
yes i think
Vocaloid
  • Vocaloid
the pattern is that each consecutive term gets multiplied by (1/3), with me so far?
rissaunnie
  • rissaunnie
yah
Vocaloid
  • Vocaloid
good. so the common ratio is (1/3) and the first term is 3^0, which is also equal to 1. there are 10 terms in the series (0,1,2,3,4,5,6,7,8,9)
Vocaloid
  • Vocaloid
so we plug a = 1 r = (1/3) n = 10 into this equation:
Vocaloid
  • Vocaloid
|dw:1447364174605:dw|
Vocaloid
  • Vocaloid
to get:|dw:1447364220721:dw|
Vocaloid
  • Vocaloid
it only asks for the equation, so I presume that would be sufficient
rissaunnie
  • rissaunnie
thank yyou cx

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