Question 986764
.
A certain arithmetic sequence has  {{{a[5]}}} = -10  and  {{{a[12]}}} = 18.  Find  {{{a[2]}}}  and  {{{a[17]}}}.
-------------------------------------------------------------------------------------------


According to the condition,


{{{a[5]}}} = {{{a[1]}}} + {{{(5-1)*d}}} = {{{a[1]}}} + {{{4*d}}} = -10           (1)     and


{{{a[12]}}} = {{{a[1]}}} + {{{(12-1)*d}}} = {{{a[1]}}} + {{{11*d}}} = 18.       (2)


By distracting (1) from (2) you get


(11 - 4)*d = 18 - (-10),


7d = 28.


Hence,  d = {{{28/7}}} = 4  (the common difference of the arithmetic progression). 


Now from  (1)  you will easily find  {{{a[1]}}} = -10 - 4*4 = -26.


From this point,  complete yourself the remaining part.