The 3rd and 8th term of AP are 9 and 26 respectived. Find
Common different
First term
d = (26-9)/(8-3) = 17/5
a = 9-2d = 11/5
In AP:
an = a + ( n - 1 ) d
where
a = initial term
d = common difference
In this case:
a3 = 9
a + 2 d = 9
a8 = 26
a + 7 d = 26
a8 - a3 = a + 7 d - ( a + 2 d )
26 - 9 = a + 7 d - a - 2 d
17 = 5 d
5 d = 17
d = 17 / 5
Put this value in equation:
a + 2 d = 9
a + 2 ∙ 17 / 5 = 9
a + 34 / 5 = 9
a + 34 / 5 = 45 / 5
a = 45 / 5 - 34 / 5
a = 11 / 5