Question

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 [1]

Answer 1

Step-by-step explanation:

Given  

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

• We know that in an A.P, a is the first term and d is the common difference.
• Sum to n terms of an A.P will be n/2 (2a + (n – 1)d)
• Given S11 = 33
• So n/2 (2a + (n – 1)d) = 33
• 11/2 (2a + (11 – 1)d) = 33
• 11/2 (2a + 10d) = 33
• 11 (2a + 10d) = 66
• Or a + 5d = 3
• As every alternate term is an integer and sum is positive
• So a + 3d = 2
• Solving we get 2d = 1, or d = 1/2  
• So a = 2 – 3(1/2)
• Or a = 1/2  

Therefore a4 = a + 3d

                       = 1/2 + 3(1/2 )

                          = 2

Reference link will be

https://brainly.in/question/13799537

Answer 2

Step-by-step explanation:

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