bamboola1 bamboola1
  • 14-03-2020
  • Mathematics
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What is the sum of all even numbers 0-175 in algebraic form? If n49=99

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 22-03-2020

Answer:

[tex]S_{88}=7656[/tex]

Step-by-step explanation:

We want to find the sum of all even numbers from 0 to 175.

The series will be:

[tex]0+2+4+6+...+174[/tex]

The explicit formula for this is [tex]a_n=2n-2[/tex], where [tex]n\ge1[/tex].

We need to find how many terms are there.

[tex]2n-2=174[/tex]

[tex]2n=176\\n=88[/tex]

The sum of terms is given by:

[tex]S_n=\frac{n}{2}(a_1+l)[/tex]

Substitute n=88, [tex]a_1=0[/tex] and l=174 to get:

[tex]S_{88}=\frac{88}{2}(0+174)\\S_{88}=44*174\\S_{88}=7656[/tex]

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