Question

Interpolando-se cinco meios geométricos entre 4 e 2916,nessa ordem,a soma dos cinco termos interpolados é:
A)1452
B)3280
C)4372
D)1092
E)3028

Answer 1

$\sf{a_7=2916~~a_1=4}\\\sf{a_7=a_1\cdot q^6}\\\sf{2916=4\cdot q^6}\\\sf{q^6=\dfrac{2916}{4}}\\\sf{q^6=729}\\\sf{q=\sqrt[6]{729}}\\\sf{q=3}\\\sf{(4,\underline{12},\underline{36},\underline{108},\underline{324},\underline{972},2916}\\\sf{\sum_{termos~interpolados}=12+36+108+324+972=1452\checkmark}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\maltese~alternativa~A}}}}}$