Jamal got a job working on a assembly line in a toy factory, on the 20th day of work, he assembled 137 toys, he noticed that since he started , every day he assembed 3 more toys then the day before , how many toys did jamal assemble all together during his first 20 days
2170 toys
Well, it sounds like Jamal's toy assembly skills are going up and up. Let's figure out how many toys he assembled during his first 20 days, shall we?
On the first day, let's say Jamal assembled x toys. Since he's assembling 3 more toys every day, on the second day he assembled x + 3 toys, then x + 6 toys on the third day, and so on.
If we add up the number of toys Jamal assembled each day for 20 days, we get:
x + (x + 3) + (x + 6) + ... + (x + 3(n-1))
Now, the sum of an arithmetic sequence can be calculated using the formula:
S = (n/2)(2a + (n - 1)d)
Where S is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference.
In Jamal's case, a = x, n = 20 (since he's working for 20 days), and d = 3 (since he's assembling 3 more toys every day).
So, the sum of the toys he assembled during the 20 days would be:
S = (20/2)(2x + (20 - 1)3)
S = 10(2x + 19(3))
S = 10(2x + 57)
S = 20x + 570
Now, we know that on the 20th day, Jamal assembled 137 toys. So, we can set up an equation:
20x + 570 = 137
20x = 137 - 570
20x = -433
x = -433/20
Now, it seems there's a problem! Negative toys don't quite exist, and our calculations led us there. So either we made an error, or Jamal has some serious Houdini skills with disappearing toys. Let's investigate further to see where things went wrong.
To calculate the total number of toys Jamal assembled during his first 20 days of work, we need to determine the total number of toys he assembled each day and then add them up.
On the first day, Jamal assembled x toys.
On the second day, he assembled x + 3 toys.
On the third day, he assembled x + 3 + 3 = x + 6 toys.
This pattern continues until the 20th day, where he assembled x + (20-1) * 3 = x + 57 toys.
Now, we know that on the 20th day, he assembled 137 toys. So we can write the equation as follows:
x + 57 = 137
To solve for x, we subtract 57 from both sides of the equation:
x = 137 - 57
x = 80
So on the first day, Jamal assembled 80 toys.
Now, to find the total number of toys he assembled during his first 20 days, we can use the formula for the sum of an arithmetic sequence:
S = (n/2)(2a + (n-1)d)
Here, n is the number of terms (20), a is the first term (80), and d is the common difference (3).
S = (20/2)(2*80 + (20-1)*3)
S = 10(160 + 19*3)
S = 10(160 + 57)
S = 10(217)
S = 2170
Therefore, Jamal assembled a total of 2170 toys during his first 20 days of work.
To find out how many toys Jamal assembled in total during his first 20 days of work, we can use arithmetic progression.
First, let's find the number of toys Jamal assembled on the first day. We know that on the 20th day, he assembled 137 toys, so we can subtract 3 toys for each of the 19 preceding days:
Number of toys assembled on the first day = 137 - (3 * (20 - 1)) = 137 - (3 * 19) = 137 - 57 = 80.
Now, we can use the formula for the sum of an arithmetic progression to find the total number of toys assembled during the first 20 days:
Sum = (n / 2)(2a + (n - 1)d),
where:
- n is the number of terms (in this case, n = 20)
- a is the first term (in this case, a = 80, the number of toys assembled on the first day)
- d is the common difference (in this case, d = 3, the additional toys assembled per day)
Using the formula:
Sum = (20 / 2)(2 * 80 + (20 - 1) * 3) = 10 * (160 + 19 * 3) = 10 * (160 + 57) = 10 * 217 = 2170.
Therefore, Jamal assembled a total of 2170 toys during his first 20 days of work.
easy ...
d = 3 and
term20 = 137
a+19d = 137
a + 57 = 137
a = 80
now take the sum of first 80 terms