determine the formula for the Nth term of the following sequences, 2,3,6,11,18...

Question

solomonzelman · Answer

$\large\color{slate}{  3=1^2+2                   }$
$\large\color{slate}{  6=2^2+2                   }$
$\large\color{slate}{  11=3^2+2                   }$
$\large\color{slate}{  18=4^2+2                   }$

solomonzelman · Answer

converting this to a sequence notation, we get:

$\large\color{slate}{  a_2 =(2-1) ^2+a_1          }$
$\large\color{slate}{  a_3 =(3-1) ^2+a_1          }$
$\large\color{slate}{  a_4 =(4-1) ^2+a_1         }$
$\large\color{slate}{  a_5 =(5-1) ^2+a_1         }$

solomonzelman · Answer

$\large\color{slate}{  a_n=      }$    .....       ??

anonymous · Answer

an =1^2 ? @SolomonZelman