Find a2 and a3.

Question

a₁=2

a_n=–10a_n–1

Answer 1

1) Take the equation: a_n = -10a_n-1

2) Insert 2 for n and you get the following: a₂ = -10a_2-1

3) Rewrite equation as: a₂ = -10a₁

4) Substitute in 2 for a₁, result: a₂ = -10(2)

5) a₂ = -20 <---1st Answer!!

6) Now use this answer to answer the next question!

7) a₃ = -10a_3-1 which is a₃ = -10a₂

8) Substitute in the value of a₂ = -20.

9) a₃ = -10(-20) = 200. <---- 2nd Answer!!

Answer 2

a₂=a₁*10 = 20

You should now easily get a_3.

BTW this is a geometric sequence with a₁=22 and r =10.