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Step-by-step explanation:

The n th term ( explicit formula ) of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = - 95 and a₃₇ = - 270 , then

a₁ + 11d = - 95 → (1)

a₁ + 36d = - 270 → (2)

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

25d = - 175 ( divide both sides by 25 )

d = - 7

Substitute d = - 7 into (1) and solve for a₁

a₁ + 11(- 7) = - 95

a₁ - 77 = - 95 ( add 77 to both sides )

a₁ = - 18 , thus

= - 18 - 7(n - 1) = - 18 - 7n + 7 = - 7n - 11

= - 7n - 11 ← explicit formula

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The recursive formula allows a term in the sequence to be found by adding the common difference d to the previous term, thus

= - 7 with a₁ = - 18 ← recursive formula

18.75 gallons

step-by-step explanation: