Question

Write the first five terms of each of the sequences in obtain the corresponding series :

$a_1=a_2=2,a_n=a_{n-1}-1,n>2$

Answer 1

Here $a_1=a_2=2and{a}_n=a_{n-1}-1,$

Putting n = 3, 4 and 5, we have

$a_3=a_{3-1}-1=a_{2-1}=2-1=1[\therefore a_2=2]$

$a_4=a_{4-1}-1=a_{3-1}=1-1=0[\therefore a_3=1]$

$a_5=a_{5-1}-1=a_{4-1}=0-1=-1[\therefore a_4=0]$

Thus, first five terms of the sequence are :

2, 2, 1, 0 and -1.

The corresponding series is

2 + 2 + 1 + 0 + (-1) + ,,,