The nth term, Tn of a progression is given by Tn=2n+3. Express Tn-1 in terms of n. Show the progression is a geometric progression

Question

Related to geometric progression. 

Answer 1

T_n=2n+3

T_n-1=2(n-1)+3=2n+1

 

Let see a few members of the {Tn}.

T1=5

T2=7

T3=9

So,

T2=T1+2

T3=T2+2=T1+2*2

T4=T3+2=T2+3*2

...

T_n=T_n-1+2(n-1)

This is arithmetic progression but not geometric.

 

BUT if T_n=2ⁿ+3 it might be.