Question

Which of the following are arithmetic sequences? Check all that apply.

A. 1, 1, 2, 5, 8, 13

B. 5, 5, 5, 5, 5

C. 3, 6, 9, 12, 15

D. 2, 4, 8, 16, 32

Answer 1

The correct answer is C. 3, 6, 9, 12, 15 because an arithmetic sequence must have a constant change in the consecutive terms.

Answer 2

The correct option is B) 5, 5, 5, 5, 5 and C) 3, 6, 9, 12, 15 are arithmetic sequences

Explanation:

Arithmetic sequence is: a, a+r, a+2r, a+3r, a+4r, ....... where r is common difference

Check part A) 1, 1, 2, 5, 8, 13

In which
`a_1=1,\, a_2=1,\,a_3=2,\,a_4=5`

common difference
`d=a_n+1 -a_n`

`d=a_2 -a_1 =1-1=0`

`d=a_3 -a_2 =2-1=1`

since common difference is not same

so, sequence 1, 1, 2, 5, 8, 13 is not arithmetic sequences.

Check part B) 5, 5, 5, 5, 5

In which
`a_1=5,\, a_2=5,\,a_3=5,\,a_4=5`

common difference
`d=a_n+1 -a_n`

`d=a_2 -a_1 =5-5=0`

`d=a_3 -a_2 =5-5=0`

since common difference is same

so, sequence 5, 5, 5, 5, 5 is arithmetic sequences.

Check part C) 3, 6, 9, 12, 15

In which
`a_1=3,\, a_2=6,\,a_3=9,\,a_4=12`

common difference
`d=a_n+1 -a_n`

`d=a_2 -a_1 =6-3=3`

`d=a_3 -a_2 =9-6=3`

since common difference is same

so, sequence 3, 6, 9, 12, 15 is arithmetic sequences.

Check part D) 2, 4, 8, 16, 32

In which
`a_1=2,\, a_2=4,\,a_3=8,\,a_4=16`

common difference
`d=a_n+1 -a_n`

`d=a_2 -a_1 =4-2=2`

`d=a_3 -a_2 =8-4=4`

since common difference is not same

so, sequence 2, 4, 8, 16, 32 is not arithmetic sequences.

Therefore, the correct option is B) 5, 5, 5, 5, 5 and C) 3, 6, 9, 12, 15 are arithmetic sequences