The sequence 3/4,-3/2, 3, -6 is the arithmetic sequence.
The difference between two successive terms of an arithmetic progression is known as a common difference.
(a)
We will find the common difference between each term of the given sequences by subtracting a term and its previous term.
[tex](\frac{6}{11}- \frac{-7}{11}) \neq (\frac{-5}{11} -\frac{6}{11} )\neq (\frac{4}{11} -\frac{-5}{11})[/tex]
[tex]\frac{13}{11}\neq \frac{-11}{11}\neq \frac{9}{11}[/tex]
So, option (a) is incorrect.
(b)
We will take the common difference between the terms.
[tex](\frac{-3}{5} -\frac{-3}{4} )\neq (\frac{-3}{6} -\frac{-3}{5} )\neq (\frac{-3}{7} -\frac{-3}{6} )\\[/tex]
[tex]\frac{3}{20} \neq \frac{3}{30}\neq \frac{3}{42}[/tex]
So, option (b) is also incorrect.
(c)
We will take the common difference between the terms.
[tex](2-\frac{1}{2} )= ( \frac{7}{2}-2 )= (5 - \frac{7}{2} )[/tex]
[tex]\frac{3}{2}= \frac{3}{2} = \frac{3}{2}[/tex]
Since the difference between the terms is common.
Thus, option (c) is correct.
(d)
We will take the common difference between the terms.
[tex](\frac{-3}{2}- \frac{3}{4})\neq (3-\frac{3}{2})\neq (-6-3)[/tex]
[tex]\frac{-18}{2}\neq \frac{9}{2}\neq (-9)[/tex]
So, option (d) is incorrect.
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