Advertisement

Let's get more efficient with the notation:

                   term: a1 , term value: 3 + 0( 4 ) = 3  ...  term: a2 , term value: 3 + 1( 4 ) = 7  ...  term: a3 , term value: 3 + 2( 4 ) = 11  ...  term: a4 , term value: 3 + 3( 4 ) = 15  ...  term: a5 , term value: 3 + 4( 4 ) = 19

Do you see the pattern?

Check out the term number and the guy that's changing on the right...

What'sa50anda100?

                             term: a1 , term value: 3 + 0( 4 ) = 3  ...  term: a2 , term value: 3 + 1( 4 ) = 7  ...  term: a3 , term value: 3 + 2( 4 ) = 11  ...  term: a4 , term value: 3 + 3( 4 ) = 15  ...  term: a5 , term value: 3 + 4( 4 ) = 19  ...  term: a50 , term value: 3 + 49( 4 ) = 199  ...  term: a100 , term value: 3 + 99( 4 ) = 399


So, the formula for the nth term is

an = 3 + ( n - 1 )( 4 )