The first Arthmatic sequence is 23 and the 12th term is 72.

Determine the first three terms in the sequence and the nth term and also Determine the Value of 10th term

I will assume you meant to say:

The first term of an arithmetic sequence is 23 and the 12th term is 72.

So a = 23 , and a+11d = 72
23+11d = 72
11d = 49
d = 49/11

take over, all you have to do is use the formulas

To determine the first three terms in the arithmetic sequence, we need to find the common difference. The common difference is the difference between each term in the sequence.

Given:
First term (a₁) = 23
12th term (a₁₂) = 72

To find the common difference (d), we can use the formula:

d = (a₁₂ - a₁) / (n - 1)

Here, n is the position of the 12th term, which is 12.

Substituting the values into the formula, we have:

d = (72 - 23) / (12 - 1)
d = 49 / 11
d = 4.454545...

Since we usually work with whole numbers in arithmetic sequences, we can round the common difference to the nearest whole number. Therefore, the approximate common difference is 4.

Now that we have the common difference, we can find the first three terms by subtracting the common difference from each term starting from the first term:

First term (a₁) = 23
Second term (a₂) = a₁ + d = 23 + 4 = 27
Third term (a₃) = a₂ + d = 27 + 4 = 31

So, the first three terms in the sequence are 23, 27, and 31.

To find the nth term in the arithmetic sequence, we can use the formula:

aₙ = a₁ + (n - 1) * d

Substituting the values:

aₙ = 23 + (n - 1) * 4

To find the value of the 10th term (a₁₀), we substitute n = 10 into the formula:

a₁₀ = 23 + (10 - 1) * 4
a₁₀ = 23 + 9 * 4
a₁₀ = 23 + 36
a₁₀ = 59

So, the value of the 10th term is 59.