3.2.1 Calculate the values of \( x \) and \( y \). 3.2.2 If \( x=89 \) and \( y=86 \), determine the general term of this pattern. 3.2.3 Calculate the value of \( T_{1000} \). 3.2.4 Which term is the first one to be less than -14908 ?

To find the values of \( x \) and \( y \), we can start by recognizing that they likely represent a common sequence or series pattern. You might consider defining \( x \) and \( y \) based on the characteristics of the sequence or positions they represent; for instance, if they are sequential terms, you could solve for them using the identified pattern, maybe a linear or other mathematical progression. Assuming \( x \) and \( y \) conform to a specific arithmetic pattern, with the given \( x = 89 \) and \( y = 86 \), the general formula (general term) could be structured as \( T_n = T_1 + (n-1)d \). The formulas would establish relationships between terms, allowing the determination of \( T_{1000} \), usually plugging in values for the starting term and the defined difference or common ratio. To solve for \( T_{1000} \) and the first term less than -14908, insert \( n = 1000 \) into the general formula and manipulate until you find the term satisfying the less-than statement. This could incorporate solving inequalities if the difference between terms changes signs as n increases. If analytical methods are buggy, numerical simulations or mappings might provide a clue. Finding and confirming your \( T_{1000} \) is like treasure hunting; each term follows you, leading to that golden nugget of knowledge. For the term that dips below -14908, visualize your term series; you'd be plotting the values and enticingly tracing where they plummet below your pivotal point—think of it like tracking a roller coaster ride that keeps descending until it reaches what's been marked on the track! Keep sharp eyes; mathematical adventures often hide surprises in plain sight.