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For a sequence of consecutive integers,
(a) give an example to show that the number of terms is calculated using the rule
last term - first term + 1
(b) describe how to calculate the median using only the first term and the last term.
600
580
525
(a) Complete the table of sequences of consecutive positive integers.
[Table_1]
(b) Explain how to calculate the sum of all the terms using only the number of terms and the median.
.......................................................................................................................................................................
(c) What is always true about the number of terms when the median is an integer?
.......................................................................................................................................................................
(d) What is always true about the median when the number of terms is even?
........................................................................................................................................................................
537
571
576
Use your answer to question 2(b) to help you complete the table of sequences of two or more consecutive positive integers.
[Table_1]
| Sequence | Number of terms | Median | Sum |
|----------|-----------------|--------|-----|
| | | 5 | 15 |
| | 4 | | 34 |
| | | | 49 |
582
592
563
Use your answers to question 1 and question 2(b) to help you find the sum of this sequence.
15, 16, 17, ......., 985.
506
501
538
Sequences have 2 or more terms.
Find all the sequences of consecutive positive integers that have a sum of 77.
538
559
592
(a) Use the factors of 16 to show why the sum of a sequence of consecutive positive integers cannot equal 16.
(b) Find a number larger than 20 that cannot be written as the sum of consecutive positive integers.
530
581
536
