Question

The sequence -2, 1, 4, 7, 10,... is generated recursively by the equations a1 = -2 an = A) an = an-1 + 3 B) an = an-1 - 3 C) an = 2an-1 + 5 D) an = -an-1 + 3

Answer 1

`\boxed{A)\ a_n=a_(n-1)+3}`

Explanation:

`a_1=-2\\a_2=1\\a_3=4\\a_4=7\\a_5=10\\\\a_2-a_1=1-(-2)=1+2=3\\a_3-a_2=4-1=3\\a_4-a_3=7-4=3\\a_5-a_4=10-7=3\\\\\text{common difference d = 3}\\\\\left\{\begin{array}{ccc}a_1=-2\\a_n=a_(n-1)+3\end{array}\right`