show that the sequence defined by an=3n^2-5 is not an ap
plssssss i want it now
its my home work
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Answered by
134
Hi ,
We know that ,
______________________________
A list of numbers in which each term is
obtained by adding or subtracting a fixed
number to the preceeding terms , except
the first term is called an arithmetic
progression simply A.P.
The difference between any two successive
terms is the same throughout the series , this
is called common difference .
___________________________________
According to the problem given ,
an = 3n^2 - 5 ----( 1 )
Put n = 1 in equation ( 1 ),
1 ) a1 = 3× 1^2 - 5 = 3 - 5 = -2
2 ) put n = 2 in ( 1 ) ,
a2 = 3 × 2^2 - 5 = 12 - 5 = 7
3 ) put n = 3 in ( 1 ) ,
a3 = 3 × 3^2 - 5 = 27 - 5 = 22
Now ,
a2 - a1 = 7 - ( - 2 ) = 7 + 2 = 9 ---( 2 )
a3 - a 2 = 22 - 7 = 15 -------( 2 )
From ( 2 ) and ( 3 ) ,
a2 - a1 is not equals to a3 - a2
Therefore,
an is not an A. P.
I hope this helps you.
:)
We know that ,
______________________________
A list of numbers in which each term is
obtained by adding or subtracting a fixed
number to the preceeding terms , except
the first term is called an arithmetic
progression simply A.P.
The difference between any two successive
terms is the same throughout the series , this
is called common difference .
___________________________________
According to the problem given ,
an = 3n^2 - 5 ----( 1 )
Put n = 1 in equation ( 1 ),
1 ) a1 = 3× 1^2 - 5 = 3 - 5 = -2
2 ) put n = 2 in ( 1 ) ,
a2 = 3 × 2^2 - 5 = 12 - 5 = 7
3 ) put n = 3 in ( 1 ) ,
a3 = 3 × 3^2 - 5 = 27 - 5 = 22
Now ,
a2 - a1 = 7 - ( - 2 ) = 7 + 2 = 9 ---( 2 )
a3 - a 2 = 22 - 7 = 15 -------( 2 )
From ( 2 ) and ( 3 ) ,
a2 - a1 is not equals to a3 - a2
Therefore,
an is not an A. P.
I hope this helps you.
:)
Answered by
19
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