A firm projects its profit to Ksh. 350,000 for the first month, Ksh. 700,000 for the second month, Ksh. 1,050,000 for the third month and so on. What will be the total projected profit at the end of 1141 41 years?
Question
A firm projects its profit to Ksh. 350,000 for the first month, Ksh. 700,000 for the second month, Ksh. 1,050,000 for the third month and so on. What will be the total projected profit at the end of 1141 41 years?
Solution 1
The profit projection of the firm is increasing by Ksh. 350,000 each month. This forms an arithmetic sequence with a common difference (d) of Ksh. 350,000.
The first term (a) of the sequence is Ksh. 350,000.
The number of terms (n) in the sequence can be calculated by multiplying the number of years by the number of months in a year. So, n = 41 * 12 = 492 months.
The sum (S) of an arithmetic sequence can be calculated using the formula:
S = n/2 * (2a + (n-1)d)
Substituting the values into the formula gives:
S = 492/2 * (2*350,000 + (492-1)350,000) S = 246 * (700,000 + 491350,000) S = 246 * (700,000 + 171,850,000) S = 246 * 172,550,000 S = Ksh. 42,407,300,000
So, the total projected profit at the end of 41 years is Ksh. 42,407,300,000.
Solution 2
The profit projection of the firm is increasing by Ksh. 350,000 each month. This forms an arithmetic sequence with a common difference (d) of Ksh. 350,000.
The first term (a) of the sequence is Ksh. 350,000.
The number of terms (n) in the sequence can be calculated by multiplying the number of years by the number of months in a year. So, for 41 years, n = 41 * 12 = 492 months.
The sum (S) of an arithmetic sequence can be calculated using the formula:
S = n/2 * (2a + (n - 1)d)
Substituting the given values into the formula gives:
S = 492/2 * (2*350,000 + (492 - 1)350,000) S = 246 * (700,000 + 491350,000) S = 246 * (700,000 + 171,850,000) S = 246 * 172,550,000 S = Ksh. 42,407,300,000
So, the total projected profit at the end of 41 years is Ksh. 42,407,300,000.
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