Answer:
a₁ = -27
a₂ = -32
a₃ = -37
a₄ = -42
a₅ = -47
a₅₂ = -282
Step-by-step explanation:
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
Given explicit formula:
[tex]a_n=-5n-22[/tex]
To find the first 5 terms, substitute n = 1 through 5 into the given formula:
[tex]\begin{aligned}\implies a_1&=-5(1)-22\\&=-5-22\\&=-27\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=-5(2)-22\\&=-10-22\\&=-32\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=-5(3)-22\\&=-15-22\\&=-37\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_4&=-5(4)-22\\&=-20-22\\&=-42\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_5&=-5(5)-22\\&=-25-22\\&=-47\end{aligned}[/tex]
To find the 52nd term, substitute n = 52 into the given formula:
[tex]\begin{aligned}\implies a_{52}&=-5(52)-22\\&=-260-22\\&=-282\end{aligned}[/tex]
