IP1U7 Exercise Q6

The first four terms in a sequence of numbers, \({{T}_{1}}\), \({{T}_{2}}\), \({{T}_{3}}\) and \({{T}_{4}}\) are given below.

\({T_1 = 3^2 + 5}\)

\({T_2 = 4^2 + 6}\)

\({T_3 = 5^2 + 7}\)

\({T_4 = 6^2 + 8}\)

\(\vdots\)

1. State one similarity that you have observed for the value of the first four terms of the sequence of numbers. Hence, explain how the similarity mentioned is valid for all the terms in the sequence.
2. Find and simplify an expression, in terms of \(n\), for \({{T}_{n}}\).
3. Evaluate \({{T}_{100}}\).