Answer
$a_1=1$
$a_2=3$
$a_3=5$
$a_4=11$
$a_5=21$
$a_6=43$
$a_7=85$
Work Step by Step
We are given:
$a_{n}=a_{n-1}+2a_{n-2}, a_1=1, a_2=3$
We evaluate:
$a_1=1$
$a_2=3$
$a_3=a_2+2a_1=3+2*1=5$
$a_4=a_3+2a_2=5+2*3=11$
$a_5=a_4+2a_3=11+2*5=21$
$a_6=a_5+2a_4=21+2*11=43$
$a_7=a_6+2a_5=43+2*21=85$