Solution: a g. p has a first term of a, a common ratio of r and its 6th term is 768. another g. p has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r.

a = 24 and r = 2

Step-by-step explanation:

The n th term of a geometric progression is

= a, thus

= a = 768 → (1) and

a₃ = a

Simplifying gives

a = 768 → (3)

36ar² = 3456 → (4)

Divide (3) by (4)

= =

Cross- multiply

9r³ = 72 ( divide both sides by 9 )

r³ = 8 ( take the cube root of both sides )

r = = 2

Substitute r = 2 into (3)

a = 768, that is

32a = 768 ( divide both sides by 32 )

a = 24

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