The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728. Find r and n
The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728.
Find r and n
(1)a1=a=2(2)an=a⋅rn−1486=2⋅rn−1rn−1=243(3)sn−sn−1=an728−sn−1=486sn−1=728−486sn−1=242(4)sn−1=a⋅rn−1−1r−1242=2⋅243−1r−1242=2⋅242r−1r−1=2r=3(5)rn−1=2433n−1=35n−1=5n=6
r = 3 and n = 6
geometric sequence: a1=2⋅30=2a2=2⋅31=6a3=2⋅32=18a4=2⋅33=54a5=2⋅34=162a6=2⋅35=486s6=728
check:
an=a6=2⋅35=486( okay)
The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728.
Find r and n
(1)a1=a=2(2)an=a⋅rn−1486=2⋅rn−1rn−1=243(3)sn−sn−1=an728−sn−1=486sn−1=728−486sn−1=242(4)sn−1=a⋅rn−1−1r−1242=2⋅243−1r−1242=2⋅242r−1r−1=2r=3(5)rn−1=2433n−1=35n−1=5n=6
r = 3 and n = 6
geometric sequence: a1=2⋅30=2a2=2⋅31=6a3=2⋅32=18a4=2⋅33=54a5=2⋅34=162a6=2⋅35=486s6=728
check:
an=a6=2⋅35=486( okay)