8
QuizMultiple Choice

Limits as They Relate to Sequences and Series — Quiz

Question 8 • Precalculus

Which rule defines cap s sub n for A sub n is equal to 3 times 0 point 7 to the n th power ?

Answer
A
cap s sub n is equal to 2 point 1 times open paren 1 minus 0 point 7 to the n th power close paren
B
cap s sub n is equal to 7 times open paren 1 minus 0 point 7 to the n th power close paren
C
cap s sub n is equal to 2 point 1 times open paren 0 point 7 to the n th power close paren
D
cap s sub n is equal to 7 times open paren 0 point 7 to the n th power close paren

Explanation

The terms form a geometric sequence with first term A₁ = 3(0.7) = 2.1 and common ratio 0.7. The sum of the first n terms is Sₙ = 2.1(1 − 0.7ⁿ)/(1 − 0.7) = 7(1 − 0.7ⁿ). Therefore, the rule is “Sₙ equals 7 times (1 − 0.7 to the nth power).”

AI-written and checked against the verified answer.

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