Question 5

5.1 The following number pattern has a constant second difference.

5.1.1 Write down the value of the constant second difference. (1)

5.1.2 Determine an expression for the n-th term of the number pattern. (4)

5.1.3 The first forty terms of the number pattern are all prime numbers. Determine the forty-first term and show that it is not a prime number. (2)

5.1.4 Determine the units digit of the 49 999 998th (T_{49 999 998}) term.(2)

5.2 The n-th term of a number pattern is as follows:

T_n = -5n – 4 if n is an even number and T_n = -n² + 6 if n is an uneven number.

5.2.1 Determine the value of T₆ + T₇.(3)

5.2.2 Determine the value of k if T_k = -219.(5)

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