wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.

Open in App
Solution

Let the numbers in G.P. are ar,a,ar

So,

ar×a×ar=216

a3=216

a=6

And also, given

ar+2,a+8,ar+6 are in A.P.

2(a+8)=(ar+2)+(ar+6)

2(6+8)=(6+2rr)+6r+6

28r=6+2r+6r2+6r

6r220r+6=0

6r218r2r+6=0

6r(r3)2(r3)=0

(r3)(6r2)=0

r=3,r=13

Hence, putting values of and r, the required number are 18, 6, 2 or 2, 6 and 18.


flag
Suggest Corrections
thumbs-up
9
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon