Answer:
d = -3
[tex]a_{1}[/tex] = 27
Step-by-step explanation:
You have to use the formula [tex]a_{n} = a_{1} + (n - 1)d[/tex] two times, once for the 6th term and once for the 15th term
(1) [tex]12 = a_{1} + (6 - 1)d[/tex] (2) [tex]-15 = a_{1} + (15 - 1)d[/tex]
[tex]12 = a_{1} + 5d[/tex] [tex]-15 = a_{1} + 14d[/tex] Change signs and add to (1)
[tex]15 = - a_{1} - 14d[/tex]
27 = -9d
d = -3 - 15 = [tex]a_{1}[/tex] + 14(-3)
- 15 = [tex]a_{1}[/tex] - 42
[tex]a_{1}[/tex] = 27
