Suppose a nuclear reactor produce's 5 tons of radioactive waste in its first year of operation. in each year following the first, the amount of waste will increase by 1 ton.
1. Explain the significance of the sequence 5, 6, 7, ..., 24 in terms of radioactive waste produced by the reactor.
2. Explain the signficiance of the series 5+6+7 + ....+24 in terms of radioactive waste produced by the reactor.
3. FInd the sum of the series 5+6+7+...+24 and explain what this answer means in terms of radioactive waste produced by the reactor.
1. Explain the significance of the sequence 5, 6, 7, ..., 24 in terms of radioactive waste produced by the reactor.
2. Explain the signficiance of the series 5+6+7 + ....+24 in terms of radioactive waste produced by the reactor.
3. FInd the sum of the series 5+6+7+...+24 and explain what this answer means in terms of radioactive waste produced by the reactor.
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1. The sequence 5, 6, 7, ..., 24 represents the annual numbers of tons of waste that the reactor produces in its first (24-5)/1 + 1 = 20 years of operation.
For 1 <= n <= 20, the nth term of this sequence represents the number of tons of waste the reactor produces in its nth year of operation.
2. The series 5+6+7 + ....+24 represents the total number of tons of waste the reactor produces in its first 20 years of operation.
3. Since the common difference is constant, the series is an arithmetic series. Any finite arithmetic series has the property that the average of all its terms equals the average of just its first and last terms. Furthermore, in any finite series of terms, the sum of all the terms is the average of all the terms times the number of terms.
So the average of all the terms in 5+6+7+...+24 is just (5+24)/2 = 29/2.
Since there are 20 terms, the sum of the series is (29/2)(20) = 290.
The reactor produces a total of 290 tons of waste in its first 20 years of operation.
Lord bless you today!
For 1 <= n <= 20, the nth term of this sequence represents the number of tons of waste the reactor produces in its nth year of operation.
2. The series 5+6+7 + ....+24 represents the total number of tons of waste the reactor produces in its first 20 years of operation.
3. Since the common difference is constant, the series is an arithmetic series. Any finite arithmetic series has the property that the average of all its terms equals the average of just its first and last terms. Furthermore, in any finite series of terms, the sum of all the terms is the average of all the terms times the number of terms.
So the average of all the terms in 5+6+7+...+24 is just (5+24)/2 = 29/2.
Since there are 20 terms, the sum of the series is (29/2)(20) = 290.
The reactor produces a total of 290 tons of waste in its first 20 years of operation.
Lord bless you today!