Answer:
[tex]a_1 = 28[/tex]
Step-by-step explanation:
Arithmetic progression:
The nth term of an arithmetic progression is given by the following equation:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference between consecutive terms.
In this question, we have that:
[tex]a_7 = 4, d = -4[/tex]
We want to find [tex]a_1[/tex]. So
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]4 = a_1 + (7-1)(-4)[/tex]
[tex]a_1 = 4 + 24 = 28[/tex]
We have that [tex]a_1 = 28[/tex]
