if a1 = 4 and an = -2an - 1 - n then find the value of a5

Answer 1

a_n = -2a_{n - 1} - n

Let's find a₂ (so make n = 2):

a₂ = -2(a_2-1) - 2 = -2(a₁) - 2 = -2(4) - 2 = -8 - 2 = -10

Now let's find a₃ (so make n = 3):

a₃ = -2(a_3-1) - 3 = -2(a₂) - 3 = -2(-10) - 3 = 20 - 3 = 17

Now let's find a₄ (so make n = 4):

a₄ = -2(a_4-1) - 4 = -2(a₃) - 4 = -2(17) - 4 = -34 - 4 = -38

Now let's find a₅ (so make n = 5):

a₅ = -2(a_5-1) - 5 = -2(a₄) - 5 = -2(-38) - 5 = 76 - 5 = 71

Answer 2

Sequence rule:

a_n = -2 (a_n-1) - n

a₁ = 4

Then:

a₁ = 4

a₂ = -2 (4) - 2 = -8 - 2 = -10

a₃ = -2 (-10) - 3 = 20 - 3 = 17

a₄ = -2 (17) - 4 = -34 - 4 = -38

a₅ = -2 (-38) - 5 = 76 - 4 = 72

a₅ = 72