# Question 3

3.1 Given the linear pattern: 2x + 1 ; 3x + 3 ; 4x + 5 ; . . .

3.1.1 Write down the next term in the pattern. (1)

3.1.2 Write, in terms of x, the formula for Tn, the general term of the pattern. (3)

3.1.3 If the value of the 13th term of the pattern is 95, calculate the value of x. (2)

3.1.4 If x = 5, determine the largest value of n for which Tn < 158. (3)

3.2 An air-traffic control tower is constructed at an airport. The front view of the tower is
shown in the diagram below. AB, the first horizontal support from the bottom, is
7,9 m long and is secured to the ground. Additional horizontal supports are secured
parallel to AB and are 50 cm apart. Each additional support above 10 cm shorter
than the one below it. CD is the 45th horizontal support. AD and BC are lateral
supports on which the horizontal supports are secured.

3.2.1 Calculate the height (H), in cm, of the tower. (1)

3.2.2 Calculate the length, in metres, of the 45th horizontal support. (3)

3.2.3 Calculate the area, in square metres, enclosed by supports AB, BC, CD