Answer:
The common difference be 2.
Option(C) is corrct .
Step-by-step explanation:
As given
The first term of an arithmetic sequence is -5, and the tenth term is 13.
As the the terms in arithmetic sequence is in the form.
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
[tex]a_{n} = n^{th}\ term[/tex]
[tex]a_{1} = 1^{th}\ term[/tex]
d is the common difference .
As [tex]a_{1} = - 5[/tex]
n = 10
[tex]a_{10} = 13[/tex]
Put in the above
[tex]a_{10} = a_{1} + (10 - 1)d[/tex]
[tex]13 = -5 + (10 - 1)d[/tex]
[tex]13 + 5 = 9d[/tex]
[tex]18= 9d[/tex]
[tex]d = \frac{18}{9}[/tex]
d = 2
Therefore the common difference be 2.
Option(C) is corrct .
