Question 598451
the common difference is essentially the slope of an arithmetic progression.

{{{a[7]=34}}}, {{{a[18]=122}}}


leads us to 

{{{
d=(a[n]-a[m])/(n-m)=(122-34)/(18-7)=8
}}}

We can rewrite the nth term as


{{{
a[1]=a[n]-(n-1)d
}}}



Now using the 7th term we write



{{{
a[1]=34-(7-1)8=-14
}}}



nth term:


{{{a[n]=-14+(n-1)8}}}




:)