I am not sure if there is a shorter way in solving this one, but I can show you a solution only that it is a bit longer though.
Overview:
24 3
Formula:
[tex] t_{n} = t_{1} + (n-1) d [/tex]
We will focus first in: 24 3
To find d:
Substitute:
[tex] t_{n} [/tex] for 3
[tex] t_{1} [/tex] for 24
n for 4
3 = 24 + ( 4 -1 )d
3 = 24 + 3d
3 - 24 = 3d
-21 = 3d
- 21 / 3 = 3d /3
-7 = d
We already have d = -7, we will go back to the original one.
24 3
[tex] t_{n} = t_{1} + (n-1) d [/tex]
Substitute:
3 = [tex] t_{1} [/tex] + (5 - 1) -7
3 = [tex] t_{1} [/tex] + -28
3 = [tex] t_{1} [/tex] - 28
3 + 28 = [tex] t_{1} [/tex]
31 = [tex] t_{1} [/tex]
So, the common difference (d) is -7, while the first term ([tex] t_{1} [/tex]) is 31
