Question

solve the following recurrence relation Sn=2Sn-1​

Answer 1

Answer:

HELLO DEAR,

RECURRENCE RELATION: A sequence can be defined by giving a general formula for its nth term or by writing few of its term.

An alternative approach is to write the sequence by finding a relationship is called a recurrence relation.

GIVEN: Sn = 2S(n-1) { n_> 2 }

{S1= 1. }

To solve the recurrence relation.

SOLUTION: Sn= 2S(n-1)

taking n=2

S2= 2S(2-1)

S2= 2S1

S2= 2×1

S2= 2.

taking n=3

S3=2S(3-1)

S3=2S2

S3=2×2

S3=4.

taking n=4

S4=2S(4-1)

S4=2S3

S4=2×4

S4=8.

taking n=5

S5= 2S(5-1)

S5=2S4

S5=2×8

S5=16.

taking n=6

S6=2S(6-1)

S6=2S5

S6=2×16

S6=32.

Therefore the recurrence relation is

{1,2,4,8,16,32,..........}

I HOPE IT'S HELP YOU DEAR,

THANKS.