Question

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Which of the following is NOT an arithmetic sequence?

A) 4, 7, 10, 13, 16

B) 1, 2, 3, 4, 5

C) 15, 9, 3, -3, -9

D) 2, 4, 8, 16, 32

Answer 1

D) 2, 4, 8, 16, 32

Explanation:

We have given four sets of sequence.

And we have to find out which sequence is not an arithmetic sequence.

For this the given sequences should satisfy the value of common difference(d) and Arithmetic Progression formula.

A.P. Formula,

`T_n=a+(n-1)d`

Where
`T_n` = nth term of an A.P.

a = first term of an A.P.

n = number of terms.

d = common difference.

'd' is calculated by subtracting fist term from second term.

`d = second\ term-first\ term`

A) 4, 7, 10, 13, 16

`d = 7-4=3`

`d = 10-7=3`

Here d=3 and 5th term is 16.

So we find out the 5th term by using the formula of A.P. To check whether the sequence is in A.P. or not.

`T_5=4+(5-1)3=4+4*\ 3=4+12=16`

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

B) 1, 2, 3, 4, 5

`d =2-1=1`

`d =3-2=1`

Here d=1 and 5th term is 5.

`T_5=1+(5-1)1=1+4=5`

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

C) 15, 9, 3, -3, -9

`d =9-15=-6`

`d =3-9=-6`

Here d=-6 and 5th term is -9.

`T_5=15+(5-1)-6=15+4* -6=15+(-24)=-9`

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

D) 2, 4, 8, 16, 32

`d_1=4-2=2`

`d_2=8-4=4`

Here
`d_1=2\ But\ d_2=4`

The common difference between the terms is not same.

In case of
`d_1`.

`T_5=2+(5-1)2=2+4* 2=2+8=10`

In case of
`d_2`.

`T_5=2+(5-1)4=2+4* 4=2+16=18`

Here the given sequence does not fulfills the condition of being in A.P.

Hence the given sequence is not an arithmetic sequence.

Hence the correct option is D) 2, 4, 8, 16, 32.