Answer:
Step-by-step explanation:
Short Answer D
A alternates in sign. Every odd positioned entry is minus. No arithmetic progression does that.
B A jump from 19 to 111 after going up by 2s starting with 15 is not an arithmetic progression.
C Each entry is multiplied by 2 to get the next entry after the 3. That is a geometric progression. C is not the answer.
D starts at - 7 and has 4 added to it for each successive entry.
Answer:
Option D.
Step-by-step explanation:
We need to find the arithmetic sequence from the given sequences.
A sequence is called an arithmetic sequence if the difference between any two consecutive terms is constant.c In other words, the sequence has common difference.
In option a,
−10, 5, −52, 54, ...
[tex]d_1=a_2-a_1=5-(-10)=15[/tex]
[tex]d_2=a_3-a_2=-52-5=-57[/tex]
[tex]d_1\neq d_2[/tex]
This sequence is not an arithmetic sequence.
Similarly,
In option b,
15, 17,19, 111, ...
[tex]d_1=a_2-a_1=17-15=2[/tex]
[tex]d_3=a_4-a_3=111-19=92[/tex]
[tex]d_1\neq d_3[/tex]
This sequence is not an arithmetic sequence.
In option c,
3, 6, 12, 24, ...
[tex]d_1=a_2-a_1=6-3=3[/tex]
[tex]d_2=a_3-a_2=12-6=6[/tex]
[tex]d_1\neq d_2[/tex]
This sequence is not an arithmetic sequence.
In option d,
–7, –3, 1, 5, ...
[tex]d_1=a_2-a_1=-3-(-7)=4[/tex]
[tex]d_2=a_3-a_2=1-(-3)=4[/tex]
[tex]d_3=a_4-a_3=5-1=4[/tex]
[tex]d_1=d_2=d_3=4[/tex]
This sequence is an arithmetic sequence.
Therefore, the correct option is D.
