The complete question in the attached figure
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8