In an arithmetic Progression the 7th term is 36 and the 15th term is 92 find the AP
In AP:
a = initial term a
d = common difference
an = a + ( n - 1 ) d
a7 = a + 6 d = 36
a15 = a + 14 d = 92
Now solve this system.
a + 6 d = 36
-
a + 14 d = 92
___________
- 8 d = - 56
d = - 56 / - 8 = 7
a + 6 d = 36
a + 6 ∙ 7 = 36
a + 42 = 36
a = 36 - 42
a = - 6
Your AP:
an = a + ( n - 1 ) d
an = - 6 + ( n - 1 ) ∙ 7
an = - 6 + 7 ( n - 1 )