Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer 2

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