Answer:
The explicit formula for the given expression is [tex]a_n=-10+3n[/tex].
Step-by-step explanation:
The given sequence is
-7, -4, -1, 2, 5
The difference between two consecutive terms is same, therefore the given sequence is an arithmetic sequence.
The first term of the given AP is -7 and the common difference is
[tex]-4-(-7)=-4+7=3[/tex]
The explicit formula for an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is first term, d is common difference and n is number of terms.
Substitute a=-7 and d=3 in the above equation.
[tex]a_n=-7+(n-1)3[/tex]
[tex]a_n=-7+3n-3[/tex]
[tex]a_n=-10+3n[/tex]
Therefore the explicit formula for the given expression is [tex]a_n=-10+3n[/tex].
