Theory question 111
Indices and Logarithms(a) Simplify: (log2 8 + log2 16 − 4 log2 2)/log4 16
(b) The first, third and seventh terms of an Arithmetic Progression (A.P) from three consecutive terms of a Geometric Progression (G.P). If the sum of the first two terms of the A.P is 6, find its: (i) first term; (ii) common difference.
Show the model answer
Model answer
(a) (3 + 4 − 4)/2 = 3/2.
(b) (a + 2d)² = a(a + 6d) gives 4d² = 2ad, so a = 2d (d ≠ 0).
a + (a + d) = 6 gives 5d = 6.
(i) a = 12/5; (ii) d = 6/5. (Check: 12/5, 24/5, 48/5 form a G.P. with ratio 2.)
Explanation
For three G.P. terms, (middle)² = first × last.