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find 10 arithmetic means between 5 and "-17" and prove that the sum of all 10 AM is ten times the A. M between them.

find 10 arithmetic means between 5 and "-17" and prove that the sum of all 10 AM is ten times the A. M between them.

Grade:11

1 Answers

Kriti
44 Points
2 months ago
Here first term a=5, b=-17
d=(b-a)/(n+1)
d= -22/11
d=-2
A1= a+d = 5-2 = 3
A2=a+2d= 5-4 = 1
.
.
.
A10= a+10d = 5-20 = -15
Now, second part of the question
Sum of ten AM
=3+1+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)
=-60
And AM between 5 and -17 is
a+b/2
=5-17/2
=-6
Hence the sum of 10 AMs (-60) is ten times the AM (-6) inserted between them 
 

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