If a1=5 and an=-2an-1 then find the value of a6.

Answer 1

a1 = 5

an = -2an-1

for n=6

a6 = -2a5

a5 = -2a4

a4 = -2a3

a3 =-2a2

a2 = -2a1 = -2(5) = -10

a3 = -2(-10) = 20

a4 = -2a3 = -2(20) =-40

a5 = -2(-40) = 80

a6 = -2(80)= -160

the 6th term is -160

the sequence is

5,-10, 20, -40, 80, -160

it's a geometric sequence with common ratio =-2

an=a1r^(n-1) = 5r^(n-1) = 5(-2)^n-1

a6 = 5(-2)^5 = 5(-32)=-160