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 and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
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

	$lets say this numbers are$ $a, a r, {a r}^{2}$ $then : a + a r + {a r}^{2} = 19 (1)$ $also (a) (a r) ({a r}^{2}) = a^{3} r^{3} = 216$ $\Rightarrow a r = 6 (2)$ $(2) in (1) \Rightarrow a + 6 + 6 r = 19$ $or a + 6 r = 13 (3)$ $(2) in (3) \Rightarrow a + 6 (\frac{6}{a}) = 13$ $\Rightarrow a^{2} - 13 a + 36 = 0$ $\Leftrightarrow a = 4 or a = 9$ $\Rightarrow r = \frac{3}{2} or r = \frac{2}{3}$ $now you can write out two sequences .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum