Question

4. An A.P starts with a positive Fraction and every alternate term is an integer. If the
sum of the first 1l terms is 33, then the fourth term is
a) 2
b) 3
d) 6
c) 5​

Answer 1

Answer:

a)2

step by step answer:

sum of 11 terms = (11/2)(2a + 10d) = 33

=> 2a + 10d = 6

=> a + 5d = 3

d can be 1/2 , 3/2 , 5/2 as alternate number are integers

one possible solution a = 1/2 and d = 1/2

d = 3/2 will result in -ve a

there can be lot of other solutions if we take -ve values of d as well ( ignoring that case)

fourth term would be a + 3d

= 1/2 + 3/2

= 2