5
QuizMultiple Choice

Literal Equations — Quiz

Question 5 • Mathematics III

The formula cap s is equal to the fraction with numerator n times open paren A sub 1 plus A sub n close paren and denominator 2 gives the partial sum of an arithmetic sequence. What is the formula solved for A sub n ?

Answer
A
A sub n is equal to 2 cap s minus A sub 1 n plus n
B
A sub n is equal to the fraction with numerator 2 cap s plus A sub 1 n and denominator n
C
A sub n is equal to 2 cap s plus A sub 1 n plus n
D
A sub n is equal to the fraction with numerator 2 cap s minus A sub 1 n and denominator n

Explanation

Start with S = n(A₁ + Aₙ)/2. Multiply both sides by 2 and divide by n to get 2S/n = A₁ + Aₙ, then subtract A₁: Aₙ = 2S/n − A₁ = (2S − nA₁)/n. This is choice D, the formula with numerator 2S − A₁n and denominator n.

AI-written and checked against the verified answer.

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