Using arithmetic mean write seven rational numbers between 12/5 and 10/3.
Answers
Seven rational numbers between 
and 
are 
Step-by-step explanation:
To find : Using arithmetic mean write seven rational numbers between and
?
Solution :
Using arithmetic mean between and
Here,
First term is
Last term is
Number of terms n=9
The last term formula is
So, the seven rational rational number are
Therefore, seven rational numbers between and
are
#Learn more
Find rational number between 2 and 3find rational number between 2 and 3
https://brainly.in/question/11413325
Seven rational numbers between \frac{12}{5}
5
12
and \frac{10}{3}
3
10
are \frac{151}{60},\frac{79}{30},\frac{55}{20},\frac{43}{15},\frac{179}{60},\frac{31}{10},\frac{193}{60}
60
151
,
30
79
,
20
55
,
15
43
,
60
179
,
10
31
,
60
193
Step-by-step explanation:
To find : Using arithmetic mean write seven rational numbers between \frac{12}{5}
5
12
and \frac{10}{3}
3
10
?
Solution :
Using arithmetic mean between \frac{12}{5}
5
12
and \frac{10}{3}
3
10
Here,
First term is a=\frac{12}{5}a=
5
12
Last term is l=\frac{10}{3}l=
3
10
Number of terms n=9
The last term formula is l=a+(n-1)dl=a+(n−1)d
\frac{10}{3}=\frac{12}{5}+(9-1)d
3
10
=
5
12
+(9−1)d
\frac{10}{3}-\frac{12}{5}=8d
3
10
−
5
12
=8d
\frac{50-36}{15}=8d
15
50−36
=8d
d=\frac{14}{15\times 8}d=
15×8
14
d=\frac{7}{60}d=
60
7
So, the seven rational rational number are
a_2=a+da
2
=a+d
a_2=\frac{12}{5}+\frac{7}{60}a
2
=
5
12
+
60
7
a_2=\frac{144+7}{60}a
2
=
60
144+7
a_2=\frac{151}{60}a
2
=
60
151
a_3=a+2da
3
=a+2d
a_3=\frac{12}{5}+2(\frac{7}{60})a
3
=
5
12
+2(
60
7
)
a_3=\frac{12}{5}+\frac{7}{30}a
3
=
5
12
+
30
7
a_3=\frac{79}{30}a
3
=
30
79
a_4=a+3da
4
=a+3d
a_4=\frac{12}{5}+3(\frac{7}{60})a
4
=
5
12
+3(
60
7
)
a_4=\frac{12}{5}+\frac{7}{20}a
4
=
5
12
+
20
7
a_4=\frac{55}{20}a
4
=
20
55
a_5=a+4da
5
=a+4d
a_5=\frac{12}{5}+4(\frac{7}{60})a
5
=
5
12
+4(
60
7
)
a_5=\frac{12}{5}+\frac{7}{15}a
5
=
5
12
+
15
7
a_5=\frac{43}{15}a
5
=
15
43
a_6=a+5da
6
=a+5d
a_6=\frac{12}{5}+5(\frac{7}{60})a
6
=
5
12
+5(
60
7
)
a_6=\frac{12}{5}+\frac{35}{60}a
6
=
5
12
+
60
35
a_6=\frac{179}{60}a
6
=
60
179
a_7=a+6da
7
=a+6d
a_7=\frac{12}{5}+6(\frac{7}{60})a
7
=
5
12
+6(
60
7
)
a_7=\frac{12}{5}+\frac{7}{10}a
7
=
5
12
+
10
7
a_7=\frac{31}{10}a
7
=
10
31
a_8=a+7da
8
=a+7d
a_8=\frac{12}{5}+7(\frac{7}{60})a
8
=
5
12
+7(
60
7
)
a_8=\frac{12}{5}+\frac{49}{60}a
8
=
5
12
+
60
49
a_8=\frac{193}{60}a
8
=
60
193
Therefore, seven rational numbers between \frac{12}{5}
5
12
and \frac{10}{3}
3
10
are \frac{151}{60},\frac{79}{30},\frac{55}{20},\frac{43}{15},\frac{179}{60},\frac{31}{10},\frac{193}{60}
60
151
,
30
79
,
20
55
,
15
43
,
60
179
,
10
31
,
60
193