A Man earns a salary of #2500 Per annum, If a rise of #500 is given at the end of the year, Find :(a) the total amount the man will earn in 18 years. (b) the amount the man will earn in the 20th year. Solve with an Arithmetic Progressions.
I want to respond to that maths question posted by someone.
a=2500,d=500.
S18=18/2[2(2500)+(17)500].
S18=9[5000+8500].
9×13500=121,500.
Ans=121,500
T20=2500+(19)500.
T20=2500+9500.
T20=#12,000.
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My wife earns a salary D2500 per annum.If a rise of D500 given at the end of the year,find a)the total amount my wife will earn in 18 years b)the nut she will earn in 20 years
you have a and d
Now just find
S18 and T20
as done in the post below
S18=121,500 while T20=12,000
Well, let me do some math while you enjoy my joke. Why don't scientists trust atoms? Because they make up everything!
Now, let's solve the problem using an arithmetic progression.
(a) To find the total amount the man will earn in 18 years, we need to calculate the sum of the arithmetic progression with the first term being #2500 and the common difference being #500.
The formula to find the sum of an arithmetic progression is: S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
In this case, n = 18, a = #2500, and d = #500.
Plugging in the values, we get: S = (18/2)(2(#2500) + (18-1)(#500))
= 9(5000 + 17*500)
= 9(5000 + 8500)
= 9(13500)
= #121,500.
So, the total amount the man will earn in 18 years is #121,500.
(b) To find the amount the man will earn in the 20th year, we can use the formula for the nth term of an arithmetic progression: a_n = a + (n-1)d.
In this case, n = 20, a = #2500, and d = #500.
Plugging in the values, we get: a_20 = #2500 + (20-1)(#500)
= #2500 + 19(#500)
= #2500 + 19*500
= #2500 + 9500
= #12,000.
So, the amount the man will earn in the 20th year is #12,000.
I hope that answers your question! If you have any more, feel free to ask.
To solve this problem, we can use the concept of Arithmetic Progression (AP) to find the total amount earned by the man in a given number of years.
In an Arithmetic Progression, each term is obtained by adding a constant difference (d) to the previous term. In this case, the constant difference is #500 as the man receives a rise of #500 at the end of each year.
(a) To find the total amount earned by the man in 18 years, we can use the formula for the sum of an Arithmetic Progression:
S = (n/2)(2a + (n-1)d)
where:
S = sum of the terms
n = number of terms
a = first term
d = common difference
In this case, the first term (a) is #2500 and the common difference (d) is #500. The number of terms (n) is 18.
Plugging these values into the formula, we get:
S = (18/2)(2(2500) + (18-1)(500))
= 9(5000 + 17(500))
= 9(5000 + 8500)
= 9(13500)
= #121,500
Therefore, the total amount the man will earn in 18 years is #121,500.
(b) To find the amount the man will earn in the 20th year, we can use the formula for the nth term of an Arithmetic Progression:
Tn = a + (n-1)d
where:
Tn = nth term
n = term number
a = first term
d = common difference
In this case, the first term (a) is #2500. We want to find the 20th term (T20), so n = 20. The common difference (d) is #500.
Plugging these values into the formula, we get:
T20 = 2500 + (20-1)(500)
= 2500 + 19(500)
= 2500 + 9500
= #12,000
Therefore, the amount the man will earn in the 20th year is #12,000.