Question 2

2.1 7 ; x ; y ; —11 ; … is an arithmetic sequence. Determine the values of x and y. (4)

2.2 Given the quadratic number pattern:    —3 ; 6 ; 27 ; 60 ; …

2.2.1 Determine the general term of the pattern in the form T_n = an ²+ bn + c . (4)

2.2.2 Calculate the value of the 50^th term of the pattern. (2)

2.2.2 Show that the sum of the first n first-differences of this pattern can be given by S_n = 6n² + 3n.(3)

2.2.4 How many consecutive first-differences were added to the first term of the quadratic number pattern to obtain a term in the quadratic number pattern that has a value of 21 060? (4)

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