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Mr. Ade borrows ₦ 530.00 in the first month. Each month after that, he borrows ₦ 15.00 more than the previous month. How much will he have borrowed in total after 12 months?

Mathematics

ScanSolve AI Answer

Answer

₦ 7350.00\text{₦ 7350.00}

Step-by-step solution

3 steps

Okay ~Gracina~, let's calculate Mr. Ade's total debt.

This problem describes an arithmetic progression, where Mr. Ade's monthly borrowing increases by a constant amount.

  1. Identify the first term, common difference, and number of terms.

    The sequence of borrowings is ₦ 530.00, ₦ 545.00, ₦ 560.00, ...
    The first term (aa) is the amount borrowed in the first month:

    a=530a = 530

    The common difference (dd) is the difference between consecutive terms:

    d=545−530=15d = 545 - 530 = 15 d=560−545=15d = 560 - 545 = 15

    The total debt is for "a year", which means 12 months. So, the number of terms (nn) is:

    n=12n = 12
  2. Use the formula for the sum of an arithmetic progression.

    The sum of the first nn terms of an arithmetic progression (SnS_n) is given by the formula:

    Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n-1)d]
  3. Substitute the values and calculate the total debt.

    Substitute a=530a=530, d=15d=15, and n=12n=12 into the formula:

    S12=122[2(530)+(12−1)15]S_{12} = \frac{12}{2}[2(530) + (12-1)15] S12=6[1060+(11)15]S_{12} = 6[1060 + (11)15] S12=6[1060+165]S_{12} = 6[1060 + 165] S12=6[1225]S_{12} = 6[1225] S12=₦ 7350.00S_{12} = \boxed{\text{₦ 7350.00}}
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