Here are the problems from the image you provided, along with solutions for each:

7. Rekrutmen pegawai:

• Januari: 200 pegawai, Februari: 240 pegawai, Maret: 280 pegawai (deret aritmatika).
• Suku pertama ($a$) = 200, beda ($b$) = 40.
• Jumlah pegawai selama 12 bulan:

$S_n = \frac{n}{2} \times (2a + (n-1)b)$ $S_{12} = \frac{12}{2} \times (2(200) + (12-1)(40))$ $S_{12} = 6 \times (400 + 440) = 6 \times 840 = 5040$

Jawaban: 5,040 pegawai.

8. Pertumbuhan bakteri:

• Awal ($t=0$): 100 bakteri. Waktu membelah setiap 3 jam.
• Total waktu dari 02:00 hingga 14:00 = 12 jam (4 siklus pembelahan).
• Jumlah bakteri tiap pembelahan: $A = A_0 \times 2^n$, dengan $n$ = 4.

$A = 100 \times 2^4 = 100 \times 16 = 1600$

Jawaban: 1,600 bakteri.

9. Panjang kabel:

• Deret geometri, suku pertama ($a$) = 5 cm, suku terakhir ($l$) = 320 cm, jumlah suku ($n$) = 7.
• Rumus jumlah deret:

$S_n = a \frac{r^n - 1}{r - 1}, \text{cari rasio } (r).$ Hubungan antara suku pertama dan terakhir:

$a \times r^{n-1} = l \implies 5 \times r^6 = 320 \implies r^6 = 64 \implies r = 2.$

Jumlah kabel:

$S_7 = 5 \frac{2^7 - 1}{2 - 1} = 5 \times (128 - 1) = 5 \times 127 = 635 \, \text{cm}.$

Jawaban: 635 cm.

10. Jumlah deret aritmatika:

• Deret: $11 + 16 + 21 + 26 + ... + 56$.
• $a = 11$, $b = 5$, suku terakhir ($U_n$) = 56.

$U_n = a + (n-1)b \implies 56 = 11 + (n-1)5 \implies 45 = (n-1)5 \implies n = 10.$

Jumlah ($S_n$):

$S_n = \frac{n}{2} \times (a + U_n) = \frac{10}{2} \times (11 + 56) = 5 \times 67 = 335.$

Jawaban: 335.

Do you want more detailed explanations or need help with similar problems? Here are 5 related questions you can explore:

1. How is the formula for the sum of an arithmetic sequence derived?
2. How does the growth of a geometric sequence differ from an arithmetic one?
3. How do you solve exponential growth problems in real-life scenarios like populations?
4. Can you calculate the 15th term of a geometric sequence?
5. How do ratios work in geometric sequences?

Tip: Always identify whether a sequence is arithmetic or geometric before solving—it determines the formula you use!