Question

Numa P.G temos A5= 64 e A1= 4. Determine a razão é escreva a P.G

Answer 1

$a_n = a_m*q^{n-m}\\ a_1 = 4\\ a_5 = 64\\ a_5 = a_1*q^4\\ 64 = 4*q^4\\ q^4 = \frac{64}{4} = 16\\ q = \sqrt[4]{16}\\ q = \sqrt[4]{2^4}\\ q = 2\\ P.G: q_n = q_m*2^{n-m}$

Answer 2

an=a1.qn-1

a5=4.q5-1

64=4q4

q4=64/4

q4=16

sn=a1(qn-1)/q-1

s5=4(16^5-1)/16-1

s5=4x1.048.576-1/16-1

s5=4.194.304-1/15

s5=4.194.303/15

s5= 279.620,2