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Consider the infinite arithmetic sequence $A$ with first term $5$ and common difference $-2$. Now define the infinite sequence $B$ so that the $k^{th}$ term of $B$ is $2$ raised to the $k^{th}$ term of $A$. Find the sum of all of the terms of $B$.

 May 6, 2018
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AS = 5, 3, 1, -1, -3............etc

IS = 2^5, 2^3, 2^1, 2^-1, 2^-3

IS = 32, 8, 2, 1/2, 1/8........etc

8 / 32 = 1 / 4 - Common Ratio

Sum=F / [1 - R], where F=First term, R=Common ratio

Sum =32 / [1 - 1/4]

Sum =32 / [3/4]

Sum =32 x 4/3

Sum =42 2/3 - Sum of infinite series "B"

 May 6, 2018

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