Answer: (1) The correct option is A. (2) The correct option is C. (3) The correct option is C.
Explanation:
(1)
The given sequence is,
[tex]\frac{1}{2},\frac{1}{3} ,\frac{1}{4}[/tex]
A sequence is called an arithmetic sequence if all the terms have common difference.
[tex]\frac{1}{3} -\frac{1}{2} =\frac{2-3}{6} =\frac{-1}{6}[/tex]
[tex]\frac{1}{4} -\frac{1}{3} =\frac{3-4}{12} =\frac{-1}{12}[/tex]
The difference between terms is not same, therefore the given sequence is not arithmetic and the correct option is A.
(2)
The given sequence is,
[tex]0.3,0.9,1.5,2.1,...[/tex]
[tex]d=0.9-0.3=0.6[/tex]
The arithmetic function is defined as,
[tex]A(n)=a+(n-1)d[/tex] .... (1)
Where, a is first term and d is common difference.
The first term is 0.3 and the common difference between terms is 0.6.
[tex]A(n)=0.3+(n-1)0.6[/tex]
Therefore option C is correct.
(3)
The given sequence is,
[tex]47,32,17,2,...[/tex]
[tex]d=32-47=-15[/tex]
The first term is 47 and the common difference between terms is -15.
[tex]A(n)=47+(n-1)(-15)[/tex]
Therefore option C is correct.
