Respuesta :

semsee45

Answer:

324

Step-by-step explanation:

** The attachment shows an arithmetic sequence **

Sum of Arithmetic Series formula

[tex]S_n=\dfrac12n(a+l)[/tex]

where:

  • a = initial term
  • l = last term

[tex]a_n=2n-1[/tex]

[tex]\implies a_1=2(1)-1=1[/tex]

[tex]\implies a_{18}=2(18)-1=35[/tex]

[tex]\implies S_{18}=\dfrac12(18)(1+35)=324[/tex]

[tex]\\ \rm\Rrightarrow \sum^{18}_{n=1}2n-1[/tex]

[tex]\\ \rm\Rrightarrow 2(1)-1+2(2)-1\dots+2(18)-1[/tex]

  • a=2-1=1
  • a_18=l=36-1=35

So

[tex]\\ \rm\Rrightarrow S_n=\dfrac{n(a+l)}{2}[/tex]

[tex]\\ \rm\Rrightarrow S_n=\dfrac{18(1+35)}{2}=9(36)=324[/tex]

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