Question

find r for the geometric series S5=244 a1=4 and a5=324

Answer 1

Hello

Answer 2

a5=a1*r^4.
r^4=a5/a1=324/4=81
r=+3 or r =-3 but S5<a5.
a1=4,
a2=4*(-3)=-12;
a=3=(-12)*(-3)=+36,
a4=36*(-3)=-108
a5=(-108)*(-3)=+324
a1+a2+a3+a4+a5=4-12+36-108+324=244=s5

Answer 3

Thanks!

Answer 4

so its plus or minus 3?

Answer 5

Either or

Answer 6

Only one of the alternatives is correct. To find which one is correct, (3 or -3), substitute each into the equation for the sum of n terms of a series:
\[S _{n}=\frac{a(r ^{n}-1)}{r-1}\]
for the sum of 5 terms. Only one of the alternatives gives the correct result of 244.