jika jmlh 100 suku pertama suatu deret geo adalah 2phi dan jumlah 200suku pertama adalah 10phi maka jumlah 400 suku pertamanya adalah....

Bab Barisan dan Deret
Matematika SMP Kelas IX

Geometri
S100 = 2 π
S200 = 10 π

karena nilainya naik, maka r > 1

Sn = a x (rⁿ - 1) / (r - 1) 
S100 = a x (r¹⁰⁰ - 1) / (r - 1) = 2π
a/(r - 1) = 2π / (r¹⁰⁰ - 1)

S200 = a x (r²⁰⁰ - 1) / (r - 1) = 10 π
a/(r - 1) = 10 π /(r²⁰⁰ - 1)

a/(r - 1) = a/(r - 1)
10π/(r²⁰⁰ - 1) = 2π / (r¹⁰⁰ - 1)

***10π : 2π = 5***

r²⁰⁰ - 1 = 5 (r¹⁰⁰ - 1)
(r¹⁰⁰ + 1) (r¹⁰⁰ - 1) = 5 .(r¹⁰⁰ - 1)
r¹⁰⁰ + 1 = 5
r¹⁰⁰ = 5 - 1
r¹⁰⁰ = 4

S400 = a x (r⁴⁰⁰ - 1) / (r - 1)
S400 = a x (r²⁰⁰ + 1) (r²⁰⁰ - 1) / (r - 1)
S400 = (r²⁰⁰ + 1) . [a x (r²⁰⁰ - 1) / (r - 1))
S400 = (r¹⁰⁰ ˣ ² + 1) . 10 π
S400 = (4² + 1) . 10 π
S400 = 17 . 10π
S400 = 170 π