# Determine if the sequence is arithmetic. If it is, find the common difference

1) 35, 32, 29, 26, ... 2) −3, −23, −43, −63, ...
3) −34, −64, −94, −124, ... 4) −30, −40, −50, −60, ...
5) −7, −9, −11, −13, ... 6) 9, 14, 19, 24, ...

1)

35, 32, 29, 26,......

t1  =  35

t2  =  32

t3  =  29

d  =  t2 - t1           or          d  =  t3 - t2

=  32 - 35                          =  29 - 32

=  -3                                  =  -3

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  -3

2)
−3, −23, −43, −63,.....

t1  =  - 3

t2  =  - 23

t3  =  - 43

d  =  t2 - t1           or          d  =  t3 - t2

=  -23 + 3                          =  -43 + 63

=  - 20                               =  - 20

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  -20

3)
−34, −64, −94, −124, ...

t1  =  - 34

t2  =  - 64

t3  =  - 94

d  =  t2 - t1           or          d  =  t3 - t2

=  -64 + 34                        =  - 94 + 64

=  - 30                               =  - 30

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  -30

edited Oct 24, 2018

Contd.......

4)
−30, −40, −50, −60, ...

t1  =  - 30

t2  =  - 40

t3  =  - 50

d  =  t2 - t1           or          d  =  t3 - t2

=  -40 + 30                        =  -50 + 40

=  - 10                               =  - 10

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  -10

5)
−7, −9, −11, −13, ...

t1  =  - 7

t2  =  - 9

t3  =  - 11

d  =  t2 - t1           or          d  =  t3 - t2

=  -9 + 7                            =  -11 + 9

=  - 2                                 =  - 2

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  -2

6)
9, 14, 19, 24, ...

t1  =  9

t2  =  14

t3  =  19

d  =  t2 - t1           or          d  =  t3 - t2

=  14 - 9                            =  19 - 14

=  5                                   =  5

Above Differences are equal

Hence, Given Series is in AP

Difference (d)  =  5

1)  Series is in AP  and Difference (d)  =  -3

2)  Series is in AP  and Difference (d)  =  -20

3)  Series is in AP  and Difference (d)  =  -30

4)  Series is in AP  and Difference (d)  =  -10

5)  Series is in AP  and Difference (d)  =  -2

6)  Series is in AP  and Difference (d)  =  5.