Question

Diketahui deret ukur dengan suku pertama sama dengan 2, suku kedua sama dengan 2^(pangkat3+x), dan suku kelima sama dengan 16. Nilai x adalah....
A. -5/6
B.-4/4
Seratakan caranya juga ya!

Answer 1

Verified answer

A = 2, U2 = 2^(3 + x), U5 = 16

U5 = 16
ar^4 = 16
2.r^4 = 16
r^4 = 8
r^4 = 2^3
r = 2^(3/4)

U2 = ar
2^(3 + x) = 2 . 2^(3/4)
2^(3 + x) = 2^(1 + 3/4)
3 + x = 1 + 3/4
x = -2 + 3/4
x = -8/4 + 3/4 = -5/4

Answer 2

Verified answer

Mapel : Matematika
Kelas : IX SMP
Bab : Barisan dan Deret

Pembahasan :
Barisan Geometri..
a = 2
U2 = 2^(3 + x)
U5 = 16

U5/U1 = (ar⁴)/(a)
16/2 = r⁴
r⁴ = 8
r = ⁴√8

U2 = ar
2^(3 + x) = 2(⁴√8)
2^(3 + x) = 2^(1 + 3/4)
2^(3 + x) = 2^(7/4)
3 + x = 7/4
x = 7/4 - 3
x = 7/4 - (12/4)
x = -5/4