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Write the explicit rule of the arithmetic sequence that has a first term of 3 and a fourth term of 18

Sagot :

Answer:

[tex]a_{n}[/tex] = 5n - 2

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 a₄ = 18 , then

a₁ + 3d = 18 , that is

3 + 3d = 18 ( subtract 3 from both sides )

3d = 15 (divide both sides by 3 )

d = 5

Then

[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 ← explicit rule

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