One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What
2 answers:
Let us say there are x number of candies .
For first student,
He ate 3/20 of all candies, so 3/20 (x)
He also ate 1.2 lb of candies.
Total candies first student ate = (3/20) x +1.2
Second student ate 3/5 of all candies that is (3/5)x
He also ate 0.3 lb of candies.
Total candies second student ate = (3/5)x +0.3
Since total candies for both will be same, so equating the two expressions
x=2
So there are 2 lb of candies in total.
First student ate = 0.3 +1.2 = 1.5lb of candies.
Second student ate = 1.5 lb of candies
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The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18