Consider this option:
if the given terms are a₁=5; a₂=-4; a₁₀= -22, then
1. rule: n-th term of any arithmetic sequence is:
[tex]a_n=a_1+d(n-1), [/tex] where d - difference of this sequence.
2. using the mentioned rule
a₄=a₁+d(4-1), ⇒ -4=5+3d; ⇒ d=-3.
(a₁₀=a₁+9d=5-3*9=-22).
3. if d=-3 and a₁=5, then it is possible to make up an equation for n-th term:
[tex]a_n=5-3(n-1)=8-3n;[/tex]
a₁₀₀=8-3*100=-292.
