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dolphi86 [110]
3 years ago
8

The fourth term of an arithmetic

Mathematics
1 answer:
yulyashka [42]3 years ago
5 0

Answer:

2

Step-by-step explanation:

<u>Given AP where:</u>

  • a₄ = 2a₂ - 1
  • a₆ = 7

<u>To find</u>

  • a₁ = ?

<u>Since</u>

  • a₄ = a₁ + 3d
  • a₂ = a₁ + d
  • a₆ = a₁ + 5d

<u>Initial equations will change as:</u>

  • a₁ + 3d = 2(a₁ + d) - 1  ⇒  a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1
  • a₁ + 5d = 7 ⇒ a₁ = 7 - 5d

<u>Comparing the above:</u>

  • d + 1 = 7 - 5d
  • 6d = 6
  • d = 1

<u>Then:</u>

  • a₁ = d + 1 = 1 + 1 = 2
  • a₁ = 2

The first term is 2

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<em><u>Solution:</u></em>

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number of spelling word questions + number of vocabulary word question = 26

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<em><u>There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each</u></em>

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Therefore, we frame a equation as:

number of spelling word questions x 2 + number of vocabulary word question x 5 = 100

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<em><u>Substitute eqn 3 in eqn 2</u></em>

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