Question

Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.

Answer 1

Answer:Given Below

Explanation:

Given

`a_1=-10`

`a_n=4a_(n-1)` for n greater than equal to 2

using above equation

`a_2=4a_1=4(-10)=-40`

`a_3=4a_2=4(-40)=-160`

`a_4=4a_3=4(-160)=-640`

`a_5=4a_4=4(-640)=-2560`

`a_6=4a_5=4(-2560)=-10,240`

Answer 2

The new sequence

-40, -160, -640, -2560, -10240, -40960

Explanation:

It is given that,

aₙ = 4a₍ₙ₋₁₎ and a₁ = -10

To find the first 7 terms of the sequence

a₁ = -10

a₂ = 4a₁ = 4 * (-10) = -40

a₃ = 4a₂ = 4 * (-40) = -160

a₄ = 4a₃ = 4 * ( -160) = -640

a₅ = 4a₄ = 4 * (-640) = -2560

a₆ = 4a₅ = 4 * (-2560) = -10240

a₇ = 4a₆ = 4 * (-10240) = -40960

Therefore the new sequence

-40, -160, -640, -2560, -10240, -40960