find the sum of arthmetic progression 12,15,18,,,,,, 84,

a=12
d=3
n=?

First you have to find out how many terms there are, so find out which term number 84 is

84 = a + (n-1)d
84 = 12 + (n-1)(3)
72 = 3n - 3
3n = 75
n = 25

so now that we know we have 25 terms, just use the formula for the sum of 25 terms.

For more information in google type "wikipedia arithmetic progression"

To find the sum of an arithmetic progression, we need to know the first term (a), the common difference (d), and the number of terms (n). In this case:

a = 12
d = 3
n = ?

To find the number of terms (n), we can use the formula:

nth term (an) = a + (n - 1) * d

We know that the nth term (an) is 84. Substituting the values into the formula:

84 = 12 + (n - 1) * 3

Let's solve for n:

84 - 12 = (n - 1) * 3
72 = (n - 1) * 3

Divide both sides by 3:

72/3 = (n - 1)
24 = n - 1

Adding 1 to both sides, we get:

24 + 1 = n
25 = n

Therefore, the number of terms (n) in the arithmetic progression is 25.

Now, we can find the sum of the arithmetic progression using the formula:

Sum (S) = n/2 * (2a + (n - 1) * d)

Substituting the values we know:

S = 25/2 * (2×12 + (25 - 1) × 3)
S = 25/2 * (24 + 24 × 3)
S = 25/2 * (24 + 72)
S = 25/2 * 96
S = 1200

Therefore, the sum of the arithmetic progression is 1200.

To find the sum of an arithmetic progression, you can use the formula:

Sum = (n/2) * (2a + (n - 1)d)

In this formula:
- Sum refers to the sum of the arithmetic progression.
- n refers to the number of terms in the progression.
- a refers to the first term in the progression.
- d refers to the common difference between consecutive terms.

Given:
a = 12 (first term)
d = 3 (common difference)
We need to find n.

To find n, we can use the formula:

nth term = a + (n - 1)d

Given the last term in the progression is 84, we can substitute the values into the formula:

84 = 12 + (n - 1) * 3

Simplifying the equation, we have:

84 = 12 + 3n - 3
84 - 12 = 3n - 3
72 = 3n - 3
75 = 3n

Dividing both sides by 3:

75 / 3 = n
25 = n

So, n = 25. Now, we can substitute the values of a, d, and n into the sum formula to find the sum:

Sum = (n/2) * (2a + (n - 1)d)
= (25/2) * (2*12 + (25 - 1)*3)
= (25/2) * (24 + 24*3)
= (25/2) * (24 + 72)
= (25/2) * (96)
= 25 * 48
= 1200

Therefore, the sum of the arithmetic progression 12, 15, 18, ..., 84 is 1200.