An AP starts with a positive fraction and every alternate term is an integer . If the sum of the first 11 terms is 33, then the fourth term is what

We know that
Sum to n terms= Sn= n/2(2a + (n – 1)d)
Given that S11 = 33
Substituting the values in the above equation, w get

n/2 (2a + (n – 1)d) = 33

11/2 (2a + (11 – 1)d) = 33
11/2 (2a + 10d) = 33
11 (2a + 10d) = 66

(2a + 10d)= 6
Taking 2 as a common factor

a + 5d = 3

We know that,

As every alternate term is an integer and sum is positive
So a + 3d = 2
Solving the two equations ,

we get 2d = 1, or d = 1/2
a = 2 – 3(1/2)
a = 1/2
Hence, fourth term a4 = a + 3d

= 1/2 + 3(1/2 )

= 2

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