# Math Algebra

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The first term of a geometric progression is more than the third term by 12. The fourth term is more than the second term by 4. Find:
i.the first term a and the common ratio r.
ii. the n'th term of the progression.

• Math Algebra -

Geometric Progression: x(n) = a r^n
First term x(0) = a
Second term x(1) = ar
etc.
So
a = ar^2 +12
ar^3 = ar +4
Rearranging gives,
a(1-r^2) = 12
a(1-r^2)r = -4
Thus solve for r by dividing,

Substitute into the original to solve for a,

• Math Algebra -

Omg im really sorry. There seems to be an error. The "fifth" term of a geometric progression is more than the third term by 12.

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