Answer:
1. [tex]a_{n} =16-13n[/tex]
2. 15th term is [tex]a_{15} =-179[/tex]
3. 10th term is -114
Step-by-step explanation:
1. The nth term of the sequence is given by the formula:
[tex]a_{n} =a+(n-1)d[/tex]
Here, the first term a = 3 and the common difference d = -10 - 3 = -13
So, [tex]a_{n} =3+(n-1)(-13)[/tex]
[tex]a_{n} =3-13n+13[/tex]
[tex]=16-13n[/tex]
2. To find the 15th term, put n = 15 in [tex]a_{n} =16-13n[/tex]
[tex]a_{15} =16-13(15)[/tex]
[tex]a_{15} =16-195[/tex]
= -179
Hence, the 15th term [tex]a_{15} =-179[/tex]
3. To find the term which is -114, put [tex]a_{n} =-114[/tex] in [tex]a_{n} =16-13n[/tex] and solve for n.
-114 = 16 - 13n
13n = 16+114
13n = 130
n = 130/13
= 10
Hence, the tenth term is -114.
