Question

6. Given that (x+2), (4x+3) and (7x+24) are consecutive terms of a Geometric Progression (G.P), find:
(a) value of x;
(b) common ratio.

Accepted Answer

For consecutive G.P terms, the middle term squared equals the product of the outer terms:
(4x+3)² = (x+2)(7x+24)
16x²+24x+9 = 7x²+38x+48
9x²−14x−39 = 0
Using the quadratic formula: x = [14±√(196+1404)]/18 = [14±√1600]/18 = [14±40]/18
x = 54/18 = 3 (taking the positive root).

(a) x = 3.
Check: (x+2)=5, (4x+3)=15, (7x+24)=45. 15/5=3, 45/15=3 ✓ confirms a valid G.P.
(b) Common ratio = 3.

GCE Mathematics 2024 Theory — Question 6

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