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Safa berjualan kue secara online, pada bulan pertama rata-rata keuntungannya sebesar Rp 75.000,00 pada bulan kedua sebesar Rp 125.000,00 begitu seterusnya menurut barisan aritmatika. Besar keuntungan Safa selama setahun adalah...

Mathematics

ScanSolve AI Answer

Answer

C. Rp 4.200.000\text{C. Rp 4.200.000}

Step-by-step solution

5 steps
  1. Identify the first term and common difference of the arithmetic sequence.

    The profit in the first month (a1a_1) is Rp 75,000.00.
    The profit in the second month (a2a_2) is Rp 125,000.00.
    The common difference (dd) is the difference between consecutive terms:

    d=a2−a1=125,000−75,000=50,000d = a_2 - a_1 = 125,000 - 75,000 = 50,000
  2. Determine the number of terms.

    The question asks for the total profit over a year, which means 12 months. So, n=12n = 12.

  3. Use the formula for the sum of an arithmetic sequence.

    The sum of the first nn terms of an arithmetic sequence is given by the formula:

    Sn=n2(2a1+(n−1)d)S_n = \frac{n}{2}(2a_1 + (n-1)d)
  4. Substitute the values and calculate the total profit.

    Substitute n=12n=12, a1=75,000a_1=75,000, and d=50,000d=50,000 into the formula:

    S12=122(2×75,000+(12−1)×50,000)S_{12} = \frac{12}{2}(2 \times 75,000 + (12-1) \times 50,000) S12=6(150,000+11×50,000)S_{12} = 6(150,000 + 11 \times 50,000) S12=6(150,000+550,000)S_{12} = 6(150,000 + 550,000) S12=6(700,000)S_{12} = 6(700,000) S12=4,200,000S_{12} = 4,200,000

    The total profit for Safa during a year is Rp 4,200,000.00.

  5. Compare the result with the given options.

    The calculated total profit is Rp 4,200,000, which corresponds to option C.

    The final answer is C. Rp 4.200.000\text{C. Rp 4.200.000}.

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