Anybody know the answer?
2 answers:
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Answer:
(d) -1.83
Step-by-step explanation:
The explicit expression for the sum is ...
S = (-11/5)×(1 -(-1/5)^10)/(1 -(-1/5)) = -2.2(1 -1.024×10^-7)/1.2
S = -1.8333331456
The sum is approximately -1.83.
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<em>Additional comment</em>
For a sum of a sequence with multiplier 'a' and common ratio r, we find ...
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A calculator or spreadsheet can also find the sum for you.
What you have here is a situation with two <em>similar triangles. </em>The triangle in the lower left is similar to the triangle in the upper right - I've included an image with "cutouts" of those triangles so you can see the similarities. Similar triangles have a very important property: <em>the ratios of their corresponding sides are equivalent</em>. Here, we can set up a ratio between the sides of length 64 and x on the larger triangle, and the corresponding sides of length x and 36 on the smaller triangle. Setting the two equal to each other, we have
Multiplying both sides of the equation by 36 and x, we get
finally, we take the square root of both sides of the equation to find x:
Multiplying both sides of the equation by 36 and x, we get
finally, we take the square root of both sides of the equation to find x: