How do you write a rule for the nth term of the arithmetic sequence given a₂₀ = 240, a₁₅ = 170?

Solution:

The nth term an of an arithmetic sequence with a₁ as the first term and d as the common difference

a_n = a₁ + (n - 1)d

a₂₀ = a₁ + 19d = 240 --- (1)

a₁₅ = a₁ + 14d = 170 --- (2)

Subtracting equation (2) from (1)

⇒ 5d = 70

Divide both sides by 5

⇒ d = 14

Substituting the value of d in equation 2

⇒ a₁ + 14 (14) = 170

⇒ a₁ + 196 = 170

⇒ a₁ = 170 - 196

⇒ a₁ = -26

So we get,

⇒ a_n = -26 + (n - 1)(14)

⇒ a_n = -26 + 14n - 14

⇒ a_n = 14n - 40

Therefore, a rule for the nth term of the arithmetic sequence is a_n = 14n - 40.

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How do you write a rule for the nth term of the arithmetic sequence given a₂₀ = 240, a₁₅ = 170?

Summary:

The rule for the nth term of the arithmetic sequence given a₂₀ = 240, a₁₅ = 170 is a_n = 14n - 40.