Theory question 111
Progressions(a) The third and sixth terms of a Geometric Progression (G.P.) are 1/4 and 1/32 respectively. Find: (i) the first term and the common ratio; (ii) the seventh term.
(b) Given that 2 and −3 are the roots of the equation ax2 + bx + c = 0, find the values of a, b and c.
Show the model answer
Model answer
(a)(i) ar2 = 1/4, ar5 = 1/32; divide: r3 = 1/8 → r = 1/2
a(1/4) = 1/4 → a = 1
(ii) T7 = ar6 = (1/2)6 = 1/64
(b) (x − 2)(x + 3) = 0 → x2 + x − 6 = 0
a = 1, b = 1, c = −6
Explanation
Dividing the two term equations removes a.