math homework sequence help

The sequence above follows a pattern.

 

\(f(n)=7n\)

 

f(n) is the output of the nth term in the sequence

n is the nth term in the sequence.

 

Since we have established this pattern, we can use this to figure out the 42nd term. If we know that 7n represents the value of the sequence at the nth term in the sequence, then we can use it to find the 42nd term.

 

\(7*42=294\)

 

294 is the 42nd term in the sequence. 

The nth term is given by:

nth. term = F + (N - 1)*D, where F=First term, N=Number of terms, D=Common difference.

42nd term =7 + (42 - 1)*7

                   =7 + (41*7)

                  =7 + 287

                  =294