If where are in A.P. and
ArithmeticGeometric progression
As we learnt in
Sum of infinite terms of a GP -
- wherein
first term
common ratio
Properties of an A.P. -
If a fixed number is added to (Subtracted from) each term of a given A.P, then the resulting sequence is also an AP.
- wherein
If is an AP
then
is also an AP
and a, b, c re in A.P
x = 1+a+a2 +...
Y= 1+b+b2 +...
z=1+c+c2 +...
Now, since a, b, c are in A.P
so -a, -b, -c are in A.P
so 1-a, 1-b, 1-c, are in A.P
so in A.P
so x, y, z are in H.P
Option 1)
this option is correct
Option 2)
ArithmeticGeometric progression
this option is incorrect
Option 3)
this option is incorrect
Option 4)
this option is incorrect
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