How can we calculate the first 21 term of the progression-18 -15 -12
To calculate the first 21 terms of the progression, we first need to determine the pattern or rule between the terms.
Given that the progression starts with -18, -15, -12, it appears that each term is obtained by adding 3 to the previous term.
To calculate the first 21 terms, we can use the formula:
term(n) = initial term + (n-1) * common difference
where:
- term(n) represents the nth term in the progression.
- initial term is the first term in the progression (-18 in this case).
- common difference is the value added to each term to obtain the next term (3 in this case).
- n is the position of the term in the progression.
Using this formula, we can calculate the first 21 terms as follows:
term(1) = -18 + (1 - 1) * 3 = -18 + 0 = -18
term(2) = -18 + (2 - 1) * 3 = -18 + 3 = -15
term(3) = -18 + (3 - 1) * 3 = -18 + 6 = -12
term(4) = -18 + (4 - 1) * 3 = -18 + 9 = -9
term(5) = -18 + (5 - 1) * 3 = -18 + 12 = -6
...
term(21) = -18 + (21 - 1) * 3 = -18 + 60 = 42
Therefore, the first 21 terms of the progression are:
-18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42.
To find the first 21 terms of the given arithmetic progression (-18, -15, -12), we need to determine the common difference and use it to find each term.
Step 1: Identify the common difference:
To find the common difference, we subtract any two consecutive terms. In this case, we can subtract the second term (-15) from the first term (-18):
-18 - (-15) = -18 + 15 = -3
So, the common difference is -3.
Step 2: Calculate the terms:
Now, we can use the formula for arithmetic progression to find each term.
The formula for the nth term of an arithmetic progression is given by:
a_n = a + (n - 1) * d
where a is the first term, d is the common difference, and n is the term number.
We can now calculate the first 21 terms:
a_1 = -18 + (1 - 1) * (-3) = -18 + 0 = -18
a_2 = -18 + (2 - 1) * (-3) = -18 + (-3) = -21
a_3 = -18 + (3 - 1) * (-3) = -18 + (-6) = -24
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a_21 = -18 + (21 - 1) * (-3) = -18 + (20) * (-3) = -18 - 60 = -78
So, the first 21 terms of the given arithmetic progression are: -18, -21, -24, ..., -78.
To calculate the first 21 terms of a progression, we need to know the pattern or rule governing the progression. In this case, it seems like there is a common difference between each term.
From the given progression (-18, -15, -12), we can observe that the common difference is 3. This means that each term is obtained by adding 3 to the previous term.
To calculate the next term, we can add 3 to the previous term:
-18 + 3 = -15
-15 + 3 = -12
-12 + 3 = -9
We can continue this process to find the next terms:
-9 + 3 = -6
-6 + 3 = -3
-3 + 3 = 0
We notice that the progression will reach 0 after three more terms, and then it will repeat. Since the common difference is 3, we know that after reaching 0, the next three terms will be 3, 6, and 9, and then it will repeat.
Therefore, the pattern for the progression (-18, -15, -12) is: -18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 0, 3, 6, 9, 0, 3, 6, 9, 0, 3, 6.
So, the first 21 terms of the progression are: -18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 0, 3, 6, 9, 0, 3, 6, 9, 0, 3, 6.