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Find the sum of -50 + (-44) + (-38) + ... + 2038 + 2044.

Sagot :

Answer:

3950

Step-by-step explanation:

-50 + (-44) + (-38) + 2038 + 2044

-94 +  (-38) + 2038 + 2044

-132 + 2038 + 2044

1906 + 2044

3950
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Solution:

348950

Explanation:

  • first lets confirm, which series this is from,

( first term + third term )/2 = second term

  • (-50 + (-38) )/2 = -44
  • -44 = -44

Thus it is arithmetic series.

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

Solving step-wise:

  • a₁ = -50
  • aₙ = 2044
  • n = ? = 350
  • d = + 6

=================

  • aₙ  = a₁ + d(n-1)
  • 2044 = -50 + 6(n-1)
  • 6(n) - 6 = 2094
  • 6(n) = 2100
  • n = 350

Here,

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

[tex]\sf S_n = \dfrac{350}{2} (2(-50)+(350-1)(6))[/tex]

[tex]\sf S_n =348950[/tex]

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