1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard VII
Mathematics
Comparision of Quantities Using Exponents
For what valu...
Question
For what values of the parameter a such that
5
1
+
x
+
5
1
−
x
,
a
2
,
25
x
+
25
−
x
are three consecutive terms of an A.P.?
Open in App
Solution
As they are in A.P.
a
=
5
1
+
x
+
5
1
−
x
+
25
x
+
25
−
x
So say
5
x
=
t
then,
a
=
5
t
+
5
t
+
t
2
+
1
t
2
Now,
5
t
+
5
t
≥
10
[A.M. - G.M. Inequality ]
and
t
2
+
1
t
2
≥
2
[A.M. - G.M. Inequality ]
So,
a
≥
12
are the values which
a
can take.
Suggest Corrections
1
Similar questions
Q.
For what values of the parameter a are there values of x such that
5
1
+
x
+
5
1
−
x
,
a
/
2
,
25
x
+
25
−
x
are three consecutive terms of an A.P.?
Q.
At what values of the parameter
a
are there values of
x
such that the numbers
5
1
+
x
+
5
1
−
x
,
a
2
,
25
x
+
25
−
x
form an arithmetic progression?
Q.
Write the value of
x
for which
x
+
2
,
2
x
,
2
x
+
3
are three consecutive terms of an A.P
Q.
If
x
ϵ
R
, the numbers
5
1
−
x
+
5
1
−
x
,
a
/
2
,
25
x
+
25
−
x
form an A.P. then
′
a
′
must lie in the interval.
Q.
If
1
x
+
y
,
1
2
y
,
1
y
+
z
are the three consecutive terms of an A.P. prove that x, y, z are the consecutive terms of a G.P.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Uses of Exponents
MATHEMATICS
Watch in App
Explore more
Comparision of Quantities Using Exponents
Standard VII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app