Question

Six arithmetic means between 7 and -28?

Answer 1

n = 6 + 2 = 8

a1 = 7

an = - 28

an = a1 + (n-1).r 

7 + (8-1).r = - 28 ==> 7 - 7r = - 28

7r = - 28 - 7 ==> 7r = - 35 ==> r = - 5
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( 7, 2, - 3, - 8, - 13, - 18, - 23, - 28 )

Answer 2

Let A1 , A2, A3 , ........A6 are arithmetic means between 7 and -28

concept :-
a , A1 , A2, A3 , A4 ........An , b

A1= a + d where, d = ( b -a)/( n +1)
A2 = a + 2d
................
...............
An = a + nd

solution :-
d = ( -28 - 7)/( 6 +1)
= -35/7
= -5
now,

A1 = a + d = 7 +(-5) = 2
A2 = a +2d = 7 -10 = -3
A3 = a + 3d = 7 -15 = -8
A4 = a +4d = 7 -20 = -13
A5 = a + 5d = 7-25 = -18
A6 =a + 6d = 7-30 = -23