Gough Watkins

04/28/2023 · Elementary School

2.1 Three positive numbers are in the ratio \( 1: 3: 7 \). If 12 is added to the largest number, the three numbers form a geometric sequence. 2.1.1 Determine the values of the three numbers. 2.2 Given the quadratic pattern: \( 2 ; 6 ; 12 ; 20 ; \ldots \). 2.2.1 Write down the next two terms of the pattern 2.2.2 Determine the general formula for the pattern, in the form \( T_{n}=a n^{2}+b n+c \) 2.2.3 Does the formula determined in 2.2 .2 produce a maximum or a minimum value? Provide a reason 2.2.4 Which term in the pattern will be equal to \( 272 ? \) 2.2.5 The first difference between two consecutive terms of the quadratic pattern is 46. Determine the value of these two terms.