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If S = [tex]\frac{n}{2}[/tex](a + L), find n when, S= 640, a = 25 and L = 39

Answer :

SEMSEE45GO

Answer:

n = 20

Step-by-step explanation:

Sum of an arithmetic series

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

where:

  • a = first term
  • l = last term
  • n = number of terms

Given:

  • [tex]S_n=640[/tex]
  • [tex]a=25[/tex]
  • [tex]l=39[/tex]

Substituting the given values into the formula and solving for n:

[tex]\implies 640=\dfrac{n}{2}(25+39)[/tex]

[tex]\implies 640 \cdot 2=n(25+39)[/tex]

[tex]\implies 1280=n(25+39)[/tex]

[tex]\implies 1280=64n[/tex]

[tex]\implies n=\dfrac{1280}{64}[/tex]

[tex]\implies n=20[/tex]

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