Answer:
The first five terms are -1, -3, -6, -10, -15
Step-by-step explanation:
∵ The recursive formula is
[tex]a_{1}[/tex] = -1 , [tex]a_{n}=a_{n-1}+(-1)n[/tex] for n > 1
∵ [tex]a_{1}[/tex] is the first term
∴ The 1st term is -1
To find the 2nd term substitute n by 2
∵ [tex]a_{2}=a_{1}+(-1)(2)[/tex]
∴ [tex]a_{2}=-1+-2=-3[/tex]
∴ The 2nd term is -3
To find the 3rd term substitute n by 3
∵ [tex]a_{3}=a_{2}+(-1)(3)[/tex]
∴ [tex]a_{3}=-3+-3=-6[/tex]
∴ The 3rd term is -6
To find the 4th term substitute n by 4
∵ [tex]a_{4}=a_{3}+(-1)(4)[/tex]
∴ [tex]a_{4}=-6+-4=-10[/tex]
∴ The 4th term is -10
To find the 5th term substitute n by 5
∵ [tex]a_{5}=a_{4}+(-1)(5)[/tex]
∴ [tex]a_{5}=-10+-5=-15[/tex]
∴ The 5th term is -15
The first five terms are -1, -3, -6, -10, -15
