Question

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

fourth term is​

Answer 1

Step-by-step explanation:

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

hope it is helpful .

Thank you.