if-the-sum-of-three-consecutive-num-ber-in-a-geometric-progression-G-P-is-19-and-their-multiple-is-216-find-the-number-

Question Number 114374 by MASANJAJ last updated on 18/Sep/20

i f t h e s u m o f t h r e e c o n s e c u t i v e n u m

b e r i n a g e o m e t r i c p r o g r e s s i o n (G . P)

i s 19 a n d t h e i r m u l t i p l e i s 216 . f i n d

t h e n u m b e r

Answered by Rio Michael last updated on 18/Sep/20

lets say this numbers are

a, a r, {a r}^{2}

then : a + a r + {a r}^{2} = 19 (1)

also (a) (a r) ({a r}^{2}) = a^{3} r^{3} = 216

\Rightarrow a r = 6 (2)

(2) in (1) \Rightarrow a + 6 + 6 r = 19

or a + 6 r = 13 (3)

(2) in (3) \Rightarrow a + 6 (\frac{6}{a}) = 13

\Rightarrow a^{2} - 13 a + 36 = 0

\Leftrightarrow a = 4 or a = 9

\Rightarrow r = \frac{3}{2} or r = \frac{2}{3}

now you can write out two sequences .