Question

A sequence {an} is defined recursively, with a1 = -1, and, for n > 1, an = an-1 + (-1)n. Find the first five terms of the sequence.

Answer 1

Answer:

The first five terms are -1, -3, -6, -10, -15

Step-by-step explanation:

∵ The recursive formula is

   $a_{1}$ = -1 , $a_{n}=a_{n-1}+(-1)n$ for n > 1

∵ $a_{1}$ is the first term

∴ The 1st term is -1

To find the 2nd term substitute n by 2

∵ $a_{2}=a_{1}+(-1)(2)$

∴ $a_{2}=-1+-2=-3$

∴ The 2nd term is -3

To find the 3rd term substitute n by 3

∵ $a_{3}=a_{2}+(-1)(3)$

∴ $a_{3}=-3+-3=-6$

∴ The 3rd term is -6

To find the 4th term substitute n by 4

∵ $a_{4}=a_{3}+(-1)(4)$

∴ $a_{4}=-6+-4=-10$

∴ The 4th term is -10

To find the 5th term substitute n by 5

∵ $a_{5}=a_{4}+(-1)(5)$

∴ $a_{5}=-10+-5=-15$

∴ The 5th term is -15

The first five terms are -1, -3, -6, -10, -15