A linear pattern 12; 9; 6; … — find the general term, the tenth term, and justify by calculation whether −316 is a term. Those terms are then the first differences of a quadratic sequence, from which two unknowns are found. The second question works with a quadratic pattern: write down the fourth and fifth terms, show the general term, count the terms, find a maximum value, and prove that every first difference is even.
linear patternsgeneral termquadratic patternsfirst differencessecond differenceproof
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