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

Question

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, ...

Answer 1

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

 

Answer 2

Contd.......