Question

calcule a soma dos termos da P.G (5,15,45,...,3645)?

Answer 1

P.G.(5,15,45,.....,3645)
a n = 3645
q = a 2 / a 1
q = 15/5
q = 3
a n = a 1 . q^n - 1
3645 = 5 . (3^n - 1)
3645 / 5 = 3^n - 1
729 = 3^n - 1
3^6 = 3 ^n - 1
6 = n - 1
6 + 1 = n
7 = n
n = 7
S n = a 1 .(q^n  -  1) / q - 1
S 7 = 5 . (3^7 - 1  ) / 3 - 1
S 7 = 5 . (2187  - 1 ) / 2
S 7 = 5 . (2186) / 2
S 7 = 10930  /  2
S 7 = 5465