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Type: Multiple-Choice
Category: Sequences and Series
Level: Grade 11
Standards: HSA-SSE.B.4
Author: nsharp1
Created: 5 years ago

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Sequences and Series Question

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The following algebraic work shows the derivation of the formula for the sum of a finite geometric series,

$S_n = a((1-r^n)/(1-r))$ . Answer the following questions to give the reasons or justification for each step in the work.

$(1) \ \ S_n = a + ar + ar^2 + ... + ar^(n-2) + ar^(n-1)$

$(2) \ \ S_n r = ar + ar^2 + ar^3 + ... + ar^(n-1) + ar^n$

$(3) \ \ S_n - S_n r = a - ar^n$

$(4) \ \ S_n (1-r) = a(1-r^n)$

$(5) \ \ S_n = a ((1-r^n)/(1-r))$

Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

Are there any restrictions one should have added at the beginning of this derivation? Choose all that apply.

No, this correct as is.
Yes, this derivation is only valid for $a>0$ .
Yes, the formula found is only true if $|r|<1$ .
Yes, it must be stated that $r!=1$ .