First two numbers of the four numbers in continued proportion are
a
respectively a and
a/2
Determine the fourth number.
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Answer:
Let the number be a,b,c,d,e such that
b
a
=
c
b
=
d
c
=
e
d
=k
⇒d=ek,c=dk=ek
2
,b=ck=ck
3
,a=bk=ek
4
___ (1)
According to conditions, a×e=256
⇒ek
4
×e=256
ek
2
=16 ___ (2)
Also, b+d=40⇒ek
3
+ek=40
16k+
k
16
=40 [∵ek
2
=16]
16k
2
−40k+16=0
4k
2
−10k+4=0
k=
8
10±
100−43
=
8
10±6
=2,
2
1
When k=2,e=
4
16
=4,d=4(2)=8,c=4(4)=16
b=4(8)=32,a=4(16)=64
When k=
2
1
,e=16×4=64,d=32,c=16,b=8,a=4
∴ Numbers are 4,8,16,32,64 or 64,32,16,8,4
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