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The second term of an arithmetic sequence is 13, and the fourth term is 7. What is the 13th term?

Sagot :

Answer:

a₁₃ = - 20

Step-by-step explanation:

The nth 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 a₂ = 13 and a₄ = 7 , then

a₁ + d = 13 → (1)

a₁ + 3d = 7 → (2)

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

2d = - 6 ( divide both sides by 2 )

d = - 3

Substitute d = - 3 into (1)

a₁ - 3 = 13 ( add 3 to both sides )

a₁ = 16

Then

a₁₃ = 16 + (12 × - 3) = 16 - 36 = - 20

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