Respuesta :

manissaha129

Answer:

Let 'a' be the first term, 'r' be the common ratio and 'n' be the number of terms

Series = 2+6+18.......= 2+2•3¹+ 2•3².......= 728

Now,

[tex]Sum = \frac{a( {r}^{n} - 1) }{(r - 1)} \\ [/tex]

So,

[tex] \frac{a( {r}^{n} - 1)}{(r - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{(3 - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{2} = 728 \\ {3}^{n} - 1 = 728 \\ {3}^{n}=728+1\\ {3}^{n} = 729 \\ {3}^{n} = {3}^{6} \\ \boxed{ n = 6}[/tex]

Therefore, number of terms is 6

  • 6 is the right answer.

Its a GP given by 2+6+18

  • First term=a=2

Common ratio=r=

[tex]\\ \bull\tt\looparrowright \dfrac{6}{2}=3[/tex]

Now

[tex]\\ \bull\tt\looparrowright S_n=728[/tex]

[tex]\\ \bull\tt\looparrowright \dfrac{a(r^n-1)}{r-1}=728[/tex]

[tex]\\ \bull\tt\looparrowright \dfrac{2(3^n-1)}{3-1}=728[/tex]

[tex]\\ \bull\tt\looparrowright \dfrac{2(3^n-1)}{2}=728[/tex]

  • Cancel 2

[tex]\\ \bull\tt\looparrowright 3^n-1=728[/tex]

[tex]\\ \bull\tt\looparrowright 3^n=728+1[/tex]

[tex]\\ \bull\tt\looparrowright 3^n=729[/tex]

[tex]\\ \bull\tt\looparrowright 3^n=3^6[/tex]

[tex]\\ \bull\tt\looparrowright n=6[/tex]

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