Question 1158164


5.

{{{-3}}},{{{-10}}},{{{-17}}},{{{-24}}},...


common difference is {{{d= -7}}}
1st term {{{a[1]=-3}}}

{{{a[n]=a[1]+d(n-1)}}}
{{{a[n]=-3-7(n-1)}}}

check:
 
{{{a[1]=-3-7(1-1)=-3}}}
{{{a[2]=-3-7(2-1)=-3-7=-10}}}-> both true

then {{{32nd}}} term is

{{{a[32]=-3-7(32-1)=-3-7*31=-220}}}


6.

{{{-9}}},{{{-6}}},{{{-3}}},{{{0}}},...

common difference is {{{d= 3}}}
1st term {{{a[1]=-9}}}

{{{a[n]=-9+3(n-1)}}}

check:
{{{a[1]=-9+3(1-1)=-9}}}
{{{a[2]=-9+3(2-1)=-9+3=-6}}}
{{{a[3]=-9+3(3-1)=-9+6=-3}}}-> all true

then {{{39th}}} term will be:

{{{a[39]=-9+3(39-1)=-9+3*38=105}}}