a=2
rumus suku ke-n = Un = 3n-1
jumlah 16 suku pertama = 392
Penjelasan dengan langkah-langkah:
diket : u5 = 14
u10 = 29
ditanya : jumlah 16 suku pertama
A dan B
dijawab :
[tex](u10 - u5) = 29 - 14 \\ u5 = 15 \\ \\ b = \frac{15}{5} \\ b = 3 \\ \\ a = 14 - (5 - 1)3 \\ a = 14 - 12 \\ a = 2 \\ \\ jumlah \: suku \: 16\: pertama \: \\ = \frac{n}{2} (2a + (n - 1)b) \\ = \frac{16}{2} (2 \times 2 + (16 - 1)3) \\ = 8(4 + 45) \\ 8(49) \\ = 392[/tex]
U5 = 14
U10 = 29
a]
U5 = a + 4b
14 = a + 4b
U10 = a + 9b
29 = a + 9b
a + 9b = 29
a + 4b = 14
------------------- -
5b = 15
b = 15/5
b = 3
a + 4b = 14
a + 4(3) = 14
a + 12 = 14
a = 14 - 12
a = 2
Un = a + (n - 1)b
Un = 2 + (n - 1)(3)
Un = 2 + 3n - 3
Un = 3n - 1
b]
n = 16
Sn = n/2 × (2a + (n - 1)b)
S16 = 16/2 × (2(2) + (16 - 1)(3))
S16 = 8 × (4 + 15(3))
S16 = 8 × (4 + 45)
S16 = 8 × 49
S16 = 392
