Q.7 If a A1 A2 b are in AP then find A1/A2
Answers
Answer:
ven a,a
1
,a
2
.............a
10
,b are in A.P.
Total number of terms in the AP are 12.
Let d be the common difference.
b=a+11d
⇒d=
11
b−a
a
1
=a+d=a+
11
b−a
=
11
10a+b
a
2
=a+2d=a+2
11
(b−a)
=
11
9a+2b
a
9
=a+9d=a+9
11
(b−a)
=
11
9a+b
a
10
=a+10d=a+10
11
(b−a)
=
11
a+10b
So, a
1
+a
10
=a
2
+a
9
=..........=a+b .....(1)
Also,given a,g
1
,g
2
......g
10
,b are in GP
Let r be the common ratio
b=ar
11
⇒r=(
a
b
)
1/11
Now, g
1
=ar=a(
a
b
)
1/11
=a
10/11
b
1/11
g
2
=ar
2
=a(
a
b
)
2/11
=a
9/11
b
2/11
g
9
=ar
9
=a(
a
b
)
9/11
=a
2/11
b
9/11
g
10
=ar
10
=a(
a
b
)
10/11
=a
1/11
b
10/11
So, g
1
g
10
=g
2
g
9
....=ab ....(2)
Consider,
g
1
g
10
a
1
+a
2
+.........+a
10
+
g
2
g
9
a
2
+a
3
+.........+a
9
+...........+
g
5
g
6
a
5
+a
6
=
ab
5(a+b)+4(a+b)+3(a+b)+2(a+b)+(a+b)
=15
ab
(a+b)
=
h
30
(∴h=
a+b
2ab
)
Answer By angel701
Step-by-step explanation:
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