Question

Geometric progression
The first three terms of a geometric progression are k+4, k and 2k-15

Where k is a constant find k or the first three terms

Answer 1

For a geometric progression we know that

c/b=b/a

b² = ac

a = k+4

b = k

c = 2k-15

hence

k² = (k+4)(2k-15)

k² = 2k²-15k+8k - 60

k²-7k-60 = 0

k²-12k+5k-60=0

k(k-12)+5(k-12)=0

(k+5)(k-12)=0

therefore

k=12 (terms are 16 12 9)

k=-5 (terms are -1 -5 -25)

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