Question

Mod 8 Honors Assignment - Sequences and Series

Answer 1

The numbers in the sequence will be 40, 80, and 160.

How to get the values?

Let x be the first number in the sequence, so the first three numbers are {x, 0.5x, 0.5²x}.

Then

{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}

0.5x - 10 = x/4 + 10 + c   = x/2 - 10 = x/4 + 10 + c

2(0.5²x) + 10 = 0.5x - 10 + c = x/2 + 10 = x/2 - 10 + c

Solve the second equation for c :

x/2 + 10 = x/2 - 10 + c

c = 20

Substitute this into the first equation and solve for x :

x/2 - 10 = x/4 + 10 + 20

x/4 = 40

x = 160

Then the terms are {160, 80, 40}

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