Question

The sequence (an) is defined by a0=1 and a (n+1)= 2an +2 for n=0,1,2.... what is the value of a3?

Answer 1

Given, $a_0=1$
and $a_{(n+1)}=2a_n+2$
put n = 0,
$a_{(0+1)}=2a_0+2$
$\implies a_1=2\times1+2=4$

put n = 1
$a_{(1+1)}=2a_1+2$
$\implies a_2=2\times4+2=10$

put n = 2,
$a_{(2+1)}=2a_2+2$
$\implies a_3=2\times10+2=22$

hence, $\boxed{\bf{a_3=22}}$