# The 3rd term of the geometrical sequence is larger than the 2nd term by 36. The product of these two terms is -243. Determine the first term.

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The third term of a geometrical sequence is larger than the 2nd term by 36. The product of these two terms is -243.

Let the first term be A, the second is Ar and the third is Ar^2.

Ar^2 = Ar + 36

Ar^2*Ar = -243

=> Ar*(Ar + 36) = -243

=> Ar = -9 and Ar = -27

Ar^2 = Ar + 36

=> -9r = -9 + 36

=> r = -3 or A = 3

and -27r = -27 + 36

=> r = -1/3 or A = 81

As the third term is larger than the second by 36, there is only one value for the first term which is 3. The other value 81 is introduced due to the other solution of the quadratic equation. This can be eliminated.

**The value of the first term is 3**