The 10th term of an arithmetic progress in 28 and the 7th term is 19.calculate the 1st,2nd and 3rd terms of the progression

3 differences (7 to 10) is 9

so d = 9 / 3 = 3

the 7th term is 6 differences from the 1st term
...1st + (3 * 6) = 7th
...1st + 18 = 19

so the 1st three terms are
...1, 4, 7

Well, well, well, let's solve this puzzle with a hint of laughter, shall we?

To find the 1st, 2nd, and 3rd terms of an arithmetic progression, we need to use a magical formula:

nth term = a + (n - 1)d

Given that the 10th term is 28, we can plug in the values:

28 = a + (10 - 1)d

Now, let's solve for 'd' by using the 7th term, which is 19:

19 = a + (7 - 1)d

We have two equations with two unknowns. Use your math prowess to solve this riddle!

To find the first, second, and third terms of an arithmetic progression, we need to use the given information: the 10th term is 28 and the 7th term is 19.

First, let's find the common difference (d) of the arithmetic progression:

d = (10th term - 7th term) / (10 - 7)
= (28 - 19) / 3
= 9 / 3
= 3

Now that we have the common difference (d = 3), we can find the first term (a) of the arithmetic progression using the 7th term:

a = 7th term - (6 * d)
= 19 - (6 * 3)
= 19 - 18
= 1

Therefore, the first term of the arithmetic progression is 1.

To find the second term, we add the common difference (d = 3) to the first term (a = 1):

2nd term = 1 + 3
= 4

So, the second term of the arithmetic progression is 4.

To find the third term, we add the common difference (d = 3) to the second term:

3rd term = 4 + 3
= 7

Hence, the third term of the arithmetic progression is 7.

Therefore, the first, second, and third terms of the arithmetic progression are 1, 4, and 7, respectively.

To solve this problem, we need to find the common difference (d) between the terms of the arithmetic progression. Once we have the common difference, we can use the given terms to find the first (a₁), second (a₂), and third (a₃) terms of the progression.

Let's begin by using the formula for the nth term of an arithmetic progression:
an = a₁ + (n - 1) * d,

where an represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 7th term is 19, we can substitute these values into the formula:

19 = a₁ + (7 - 1) * d,

Simplifying the equation:
19 = a₁ + 6d.

Similarly, the 10th term is given as 28:

28 = a₁ + (10 - 1) * d,
28 = a₁ + 9d.

Now, we have two equations:

1) 19 = a₁ + 6d,
2) 28 = a₁ + 9d.

We can solve these equations simultaneously to find the values of a₁ and d.

Subtracting equation 1 from equation 2:

28 - 19 = (a₁ + 9d) - (a₁ + 6d),
9 = 3d.

Dividing both sides of the equation by 3:

d = 3.

Substituting this value of d back into equation 1:

19 = a₁ + 6(3),
19 = a₁ + 18,
a₁ = 19 - 18,
a₁ = 1.

Now that we have found a value for a₁, we can use it to find the second and third terms of the progression.

The second term (a₂) can be found by substituting n = 2 into the nth term formula:
a₂ = a₁ + (2 - 1) * d,
a₂ = a₁ + d,
a₂ = 1 + 3,
a₂ = 4.

Similarly, using n = 3:
a₃ = a₁ + (3 - 1) * d,
a₃ = a₁ + 2d,
a₃ = 1 + 2(3),
a₃ = 7.

Therefore, the first term (a₁) is 1, the second term (a₂) is 4, and the third term (a₃) is 7.