- This Investigation Looks At The Results When The Terms Of A Sequence Of Consecutive Positive Integers Are Added Together 1 (154.67 KiB) Viewed 27 times
This investigation looks at the results when the terms of a sequence of consecutive positive integers are added together. (a) The mean of 6 positive integers is 4.5. Calculate the sum of the 6 integers. (b) (i) Sequence 5, 6, 7, 8, 9, 10 10, 11, 12, ..., 40 2, 3, 4, 5, 6, 7, 8 (ii) Complete the table for sequences of two or more consecutive positive integers. (i) (ii) (iii) (e) No. of Terms ACS (Independent) Mathematics Department 6 31 35 42 49 Describe how to calculate the mean using only the first term and the last term of a sequence of consecutive integers. (i) 4 (ii) Mean 25 (c) k.k+1.k+2.....k+99 is a sequence of consecutive integers. Write down the number of terms in this sequence. Use the first term and the last term to find an expression for the mean in terms of k. expression for the Use your answers to part (i) and part (ii) to write down an sum of all the terms of the sequence. Sum of all the Terms (d) Use the method of part (c) to show that the sum of the integers n(2k+n-1) k,k+1,k+2,...,k+(n-1) is 2 If n is odd, explain why the value of the expression integer. If n is even, explain why the value of the expression (f) The sum of a sequence of consecutive positive integers is 84. (i) (ii) 2k+n-1 2 164 2k+n-1 2 must be an must end in .5 Using parts (d) and (e), find all the possible values of n and the corresponding values for the mean. Write down all the possible sequences of consecutive positive integers whose sum is 84. (g) Find a number, bigger than 20, which cannot be written as the sum of consecutive positive integers.