Question 963684
Basic Term in General for Arithmetic Sequence:
{{{A[n]=A[1]+(n-1)d}}}
A[n], general n term
A[1], first term
n, index of the term
d, common difference to each successive term



Let a be the first term of the sequence, d understood as already said;


{{{system(-17=a+(5-1)d,-47=a+(11-1)d)}}}


{{{system(a+4d=-17,a+10d=-47)}}}


Subtract corresponding equation members:
{{{6d=17-47}}}

{{{6d=-30}}}


{{{highlight(d=-5)}}}


You also want to know "a".  Use either equation from the system.
{{{a=-17-4d}}}
{{{a=-17-4(-5)}}}
{{{-17+20}}}
{{{highlight(a=3)}}}


You can find the first few terms of the sequence......!