Respuesta :

Hrishii

Answer:

6075

Step-by-step explanation:

  • Given series is: 25 + 30 + 35 + ⋯ + 245.

  • Here, first term (a) = 25
  • Common difference (d) = 5
  • Last term [tex](a_n) = 245[/tex]

  • First we find the number of terms that this series has by the following formula:

  • [tex]a_n = a+(n-1)d[/tex]

  • Plugging the values of a, d and [tex]a_n[/tex], we find.

  • [tex]245 = 25+(n-1)5[/tex]

  • [tex]\implies 245 - 25=(n-1)5[/tex]

  • [tex]\implies 220=(n-1)5[/tex]

  • [tex]\implies \frac{220}{5}=n-1[/tex]

  • [tex]\implies 44=n-1[/tex]

  • [tex]\implies 44+1=n[/tex]

  • [tex]\implies\red{\bold{ n=45}}[/tex]

  • Thus, the given series contains 45 terms.

  • Next, we find the sum of the given series using the formula given below.

  • [tex]S_n = \frac{n}{2}(a+a_n)[/tex]

  • [tex]\implies S_{45}= \frac{45}{2}(25+245)[/tex]

  • [tex]\implies S_{45}= \frac{45}{2}(270)[/tex]

  • [tex]\implies S_{45}=45*135[/tex]

  • [tex]\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}[/tex]

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