Question 1 1. The first four terms of a quadratic number pattern are -1; 2;9;20 1.1. Determine the general term rule for the number pattern. 1.2. Calculate the fourth term of the number pattern. Question 2 2. Given that 4;9;x;37;; 2949 form a quadratic number pattern. 2.1. Calculate the numerical value of x. 2.2. Hence, or otherwise determine the nth term rule of the number pattern. 2.3. Determine how many terms are in the number pattern. Question 3 3. The first three terms of an arithmetic sequence 4; 13; 22 3.1. Write down the fourth term of the sequence. 3.2. Determine the general term rule of the sequence. 3.3. Consider the terms of the sequence which are even. Calculate the sum of the first 25 terms which are even. (4) (2) (4) (4) (4) (1) (3) (4) 3.4. The original sequence (4; 13; 22) forms the first differences of a new sequence with a first term of 6. Determine the general term rule for this new sequence. (4) Question 4 4 Consider the sequence 4; 1; -2... 4.1. Determine the general term rule for the sequence. 4.2. Which term in the sequence is equal to -143?
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1, to determine the general term rule for the number pattern, we need to find the pattern in the differences between consecutive terms. Show more…
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QUESTION 2 2.1 Given the following quadratic number pattern: 5 ; -4 ; -19 ; -40 ; ... 2.1.1 Determine the constant second difference of the sequence. 2.1.2 Determine the nth term (Tn) of the pattern. 2.1.3 Which term of the pattern will be equal to -25 939? 2.2 The first three terms of an arithmetic sequence are 2k - 7 ; k + 8 and 2k - 1. 2.2.1 Calculate the value of the 15th term of the sequence. 2.2.2 Calculate the sum of the first 30 even terms of the sequence.
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3.4 The following sequence forms a quadratic number pattern: -3; -2; -3; -6; -11; ... 3.4.1 The first differences of the above sequence also form a sequence. Determine an expression for the general term of the first differences. 3.4.2 Calculate the first difference between the 35th and the 36th term of the quadratic sequence. 3.4.3 Determine an expression of the nth term of the quadratic sequence. 3.4.4 Explain why the sequence of the numbers will never contain a positive term.
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