Respuesta :

Answer:

Sum of arithmetic series is [tex]2077[/tex]

Step-by-step explanation:

We have [tex]n[/tex]th term of arithmetic sequence

[tex]a+(n-1)d[/tex]

Here

[tex]a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4[/tex]

Sum of arithmetic sequence [tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077[/tex]

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

  • »» [tex]\rm{a_1}[/tex] = 1
  • »» [tex]\rm{n}[/tex] = 31
  • »» [tex]\rm{a_n}[/tex] = 127

We need to find :

  • »» The sum of arithmetic series.

Here's the required formula to find the sum of arithmetic series :

[tex]\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

Substituting all the given values in the formula to find the sum of arithmetic series :

[tex]{\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}[/tex]

[tex]{\longrightarrow{\sf S = 31 \times 67}}[/tex]

[tex]{\longrightarrow{\sf S = 2077}}[/tex]

[tex]\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}[/tex]

Hence, the sum of arithmetic series is 2077.

[tex]\rule{300}{1.5}[/tex]

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