Theory question 107
Progressions(a) The first term of an Arithmetic Progression (AP) is 3 and the common difference is 4. Find the sum of the first 28 terms.
(b) Given that x = 2m/(1 − m2) and y = 2m/(1 + m), express 2x − y in terms of m in the simplest form.
(c) The angles of pentagon are x°, 2x°, 3x°, 2x° and (3x − 10)°. Find the value of x.
Show the model answer
Model answer
(a) S28 = 28/2 [2(3) + 27(4)] = 14 × 114 = 1596.
(b) 2x − y = 4m/(1 − m2) − 2m(1 − m)/(1 − m2) = (2m + 2m2)/(1 − m2) = 2m(1 + m)/[(1 − m)(1 + m)] = 2m/(1 − m).
(c) Angles of a pentagon add to 540°: 11x − 10 = 540, so x = 50.
Explanation
Use 1 − m² = (1 − m)(1 + m) as the common denominator.