Question

PLEASE HELP ASAP *URGENT* 20 POINTS!!!!

Answer 1

a₅ = 122

Step-by-step explanation:

What is a₅ for the sequence defined by:

`\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_(n-1)+2\\\end{array}\right\\\\\\\hrule`

Letting n=2:

`a_n=-3a_(n-1)+2\\\\\\\\\Longrightarrow a_2=-3a_(2-1)+2\\\\\\\\\Longrightarrow a_2=-3a_(1)+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4`

Letting n=3:

`a_n=-3a_(n-1)+2\\\\\\\\\Longrightarrow a_3=-3a_(3-1)+2\\\\\\\\\Longrightarrow a_3=-3a_(2)+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14`

Letting n=4:

`a_n=-3a_(n-1)+2\\\\\\\\\Longrightarrow a_4=-3a_(4-1)+2\\\\\\\\\Longrightarrow a_4=-3a_(3)+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40`

Letting n=5:

`a_n=-3a_(n-1)+2\\\\\\\\\Longrightarrow a_5=-3a_(5-1)+2\\\\\\\\\Longrightarrow a_5=-3a_(4)+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}`

Answer 2

a5 = 122

Step-by-step explanation:

Given:

• a1 = 2

• an = -3aₙ₋₁ + 2

Solve:

a1 = 2

a2 = -3a1+2 = -3(2)+2 = -4

a3 = -3a2 + 2 = -3(-4)+2 = 14

a4 = -3a3 + 2 = -3(14) + 2 = -40

a5 = -3a4 + 2 = -3(-40) + 2 = 122