Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for $n\,>\,1$
$\Rightarrow a_{2}=3 a_{1}+2=3(3)+2=11$
$a_{3}=3 a_{2}+2=3(11)+2=35$
$a_{4}=3 a_{3}+2=3(35)+2=107$
$a_{5}=3 a_{4}+2=3(107)+2=323$
Hence, the first five terms of the sequence are $3,11,35,107$ and $323$
The corresponding series is $3+11+35+107+323+\ldots$
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