# Mathematics

A GP is such that the 3rd term is nine times the 1st term while the 2nd term is one - twenty fourth of the 5th term .Find it's fourth term.

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1. This cannot be solved because:

In GP:

an = a1 ∙ r ⁿ ⁻ ¹

a2 = a1 ∙ r

a3 = a1 ∙ r²

a5 = a1 ∙ r⁴

a3 = 9 a1

a1 ∙ r² = 9 a1

Divide both sides by a1

r² = 9

r = ± √ 9

r = ± 3

a2 = a5 / 24

a1 ∙ r = a1 ∙ r⁴ / 24

Divide both sides by a1 ∙ r

1 = r³ / 24

Multiply both sides by 24

24 = r³

The result is:

24 = r³

24 = ( - 3 )³ = - 27

OR

24 = 3³ = 27

That is obviously not true.

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