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

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**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.

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**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.

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**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.

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**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.

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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!

Solve the series of arithmetic and geometric problems provided in the image, including: recruitment calculations, bacterial growth, cable lengths, and summation of arithmetic series.

Explore detailed solutions for arithmetic and geometric problems, including calculating recruitment trends, bacterial growth, geometric sequence sums, and summation of arithmetic series. Perfect for students in Grades 9-12.

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