Answered

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A linear sequence (i.e. where the 1st difference is always the same) has 5th term 6 and 92nd term 354. What is the 57th term?

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Answer:

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Answer:

a₅₇ = 214

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ = 6 and a₉₂ = 354 , then

a₁ + 4d = 6 → (1)

a₁ + 91d = 354 → (2)

Subtract (1) from (2) term by term to eliminate a₁

0 + 87d = 348

87d = 348 ( divide both sides by 87 )

d = 4

Substitute d = 4 in (1) and solve for a₁

a₁ + 4(4) = 6

a₁ + 16 = 6 ( subtract 16 from both sides )

a₁ = - 10

Then

a₅₇ = - 10 + (56 × 4 ) = - 10 + 224 = 214

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