The 7th term of an a.p is 11 and the nth term is 3. Find the first five term

Answer 1

a+6d=11
a+(n-1)d=3
subtract them:
6d - (n-1)d = 8
6d - nd + d = 8
7d - nd = 8
d = 8/(7-n) , it should be noted that n ≠ 7

back in the 1st:
a + 48/(7-n) = 11
a = 11 - 48/(7-n)
= (77 - 11n - 48)/(7-n)
= (29 - 11n)/(7-n)

so the terms are:
(29 - 11n)/(7-n) , (37 - 11n)/(7-n), ... etc

check:
term(7) = a + 6d
= (29 - 11n)/(7-n) + 48/(7-n)
= (56 - 8n)/(7-n)
= (77 - 11n) /(7-n)
= 11(7-n)/(7-n) = 11 , yeahhhh