Find the first six terms of the sequence. a1 = -8, an = 5 • an-1

Answer 1

The sequence is an=5 an-1

First term,a1 = - 8

an =5(an-1)

an/an-1 =5

It is in the form an/an-1 = r

So the sequence is geometric sequence.

So the common ratio is r = 5

a1 = -8

a2 = a1(r) = (-8)(5) = -40

a3 =a1(r²)=  (-8)(5²) =(-8)(25) =-200

a4 =a1(r³)=  (-8)(5³) =(-8)(125) =-1000

a5 =a1(r⁴)=  (-8)(5⁴) =(-8)(625) =-5000

a6 =a1(r⁵)=  (-8)(5⁵) =(-8)(3125) =-25000

Therefore, the first six terms are -8,-40,-200,-1000,-5000, and -25000