Question

Calcule a soma dos termos da PG (4096,1024,...,16).

Answer 1

a1 = 4096
a2 = 1024

an  = 16

q = a2/a1 = 1024/4096 =1/4 ****
a2 = a1.q = 1024
an  = a1 qⁿ⁻¹
16 = 4096 * (1/4 )ⁿ⁻¹
16/4096 =  ( 1/4)ⁿ⁻¹
1/256  = ( 1/4)ⁿ⁻¹
( 1/4)⁴ =( 1/4)ⁿ⁻¹
n - 1 = 4
n = 4 + 1 = 5 ***

S5 =  a1 ( qⁿ  - 1)/ ( q - 1)
S5 = 4096[ ( 1/4)⁵  - 1 ] / (  1/4 - 1/1)
S5  = 4096. [ ( 1024  - 1 ] ]/ ( - 3/4 )
S5 =( 4096 . 1023 )/ ( -3/4 )
S5 = 4190208 :( - 3/4 )  = 4190208/1 * ( - 4/3 ) = - 16760832/3 =- 5586944 ***