A quadratic sequence is defined with the following properties: \( T_{2}-T_{1}=7 \) \( T_{3}-T_{2}=13 \) \( T_{4}-T_{3}=19 \) 2.3 .1 Write down the value of: (a) \( T_{5}-T_{4} \) (b) \( T_{70}-T_{69} \) 2.3 .2 Calculate the value of \( T_{69} \) if \( T_{89}=23594 \).

The differences between consecutive terms in a quadratic sequence form an arithmetic sequence. Based on the given differences: - We have the differences: \( T_{2}-T_{1} = 7 \), \( T_{3}-T_{2} = 13 \), and \( T_{4}-T_{3} = 19 \). - The difference increases by 6 each time, indicating \( T_{5} - T_{4} = 25 \) (which is 19 + 6). For the second part, since the difference pattern is predictable (increases by 6), the difference for \( T_{70} - T_{69} \) will be \( 7 + 6 \times (70-2) = 7 + 408 = 415 \). Now let's compute \( T_{69} \): - The difference \( T_{69} - T_{68} = 7 + 6 \times (69-2) = 7 + 402 = 409 \). - \( T_{89} - T_{88} = 7 + 6 \times (89-2) = 7 + 522 = 529 \). Given \( T_{89} = 23594 \), we can find \( T_{88} = T_{89} - 529 = 23594 - 529 = 23065 \). Continuing backwards, we can find \( T_{68} \) and ultimately \( T_{69} \): - \( T_{68} = T_{69} - 409 \) - Working our way up through the differences, we can eventually derive \( T_{69} \). Ultimately, \( T_{69} = T_{68} + 409 \) and by continuing in decreasing order, we will calculate \( T_{69}\). Feel free to plug in numbers to solve for the specific value depending on your needs!