Respuesta :

mhanifa

Answer:

  • 912

Step-by-step explanation:

Given the AP

  • 3, 8, 13, 18, ...

We can see that

  • The first term is a = 3
  • The common difference is d = 5

The sum of the first n terms formula is

     [tex]S_n=\cfrac{n}{2} [2a+(n-1)d][/tex]

Substitute the values and considering n = 19, find the sum  

    [tex]S_{19}=\cfrac{19}{2} [2*3+(19-1)*5]=\cfrac{19}{2} [6+90]=912[/tex]

semsee45

Answer:

912

Step-by-step explanation:

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]

where:

  • n = nth term
  • a = first term
  • d = common difference

Given arithmetic series:  3 + 8 + 13 + 18 + ...

Therefore:

  • a = 3
  • d = 8 - 3 = 5

To find the sum of the first 19 terms, substitute the given values together with n = 19 into the Sum formula:

[tex]\implies S_{19}=\dfrac{1}{2}(19)\left[\:2(3)+5(19-1)\:\right][/tex]

[tex]\implies S_{19}=\dfrac{19}{2}\left[\:6+90\:\right][/tex]

[tex]\implies S_{19}=\dfrac{19}{2}\left[\:96\:\right][/tex]

[tex]\implies S_{19}=912[/tex]

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