The sequence shows a pattern of decreasing by 8, indicating an arithmetic sequence. The nth term equation, considering the first term and the common difference, is aₙ = -8n + 13, which is option D.
The first four terms of a sequence are given as 5, -3, -11, -19. To find the equation for the nth term of the sequence, we can identify the pattern of the sequence. Looking at the differences between the terms, we see that each term decreases by 8 compared to the previous one:
- 5 to -3 is a decrease of 8 (5 - 8 = -3)
- -3 to -11 is a decrease of 8 (-3 - 8 = -11)
- -11 to -19 is a decrease of 8 (-11 - 8 = -19)
This pattern suggests that the sequence is arithmetic with a common difference of -8. Therefore, the nth term formula would be of the form aₙ = a₁ + (n-1)d, where a₁ is the first term and d is the common difference
Using the first term (a₁ = 5) and the common difference (d = -8), we get:
aₙ = 5 + (n-1)(-8) = 5 - 8n + 8 = -8n + 13
So, the correct equation for the nth term would be aₙ = -8n + 13, which corresponds to option D.
Complete Question:
The first four terms of a sequence are 5, -3, -11, 19. Which of the following is an equation for the nth term of the sequence? A.aₙ=8n-3 B. aₙ=n-4 C. aₙ=-8n-8 D. aₙ=-8n+13