Question 1205015
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The 3rd term 4 is half of the 5th term 8, so the 1st term is half of the 3rd term, so the first term is 2.<br>
From the given information, the common ratio could be either sqrt(2) or -sqrt(2)<br>
But if the common ratio were negative, the sum of the first two terms would be negative, as would each sum of any following two terms, making the sum of the first ten terms negative.<br>
So the common ratio is sqrt(2).<br>
In the sum of the first ten terms, the sum of the odd-numbered terms is 2+4+8+16+32 = 62; so the sum of the even-numbered terms is 62*sqrt(2).<br>
ANSWERS:
common ratio: sqrt(2)
sum of first ten terms: 62+62*sqrt(2)<br>