What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?
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To find the sum of the first 4 terms of an arithmetic sequence, we first need to find the common difference (d) of the sequence.
We are given that the 6th term is 8, and the 10th term is 13. Using this information, we can find the common difference by subtracting the 6th term from the 10th term: 13 - 8 = 5.
Now that we know the common difference is 5, we can find the sum of the first 4 terms of the sequence.
The formula for the sum of the first n terms of an arithmetic sequence is: Sn = (n/2)(2a + (n - 1)d), where Sn is the sum, a is the first term, n is the number of terms, and d is the common difference.
Since we want to find the sum of the first 4 terms, we substitute a = the first term, n = 4, and d = 5 into the formula.
Substituting these values into the formula, we get: S4 = (4/2)(2a + (4 - 1)5).
Simplifying further, we have: S4 = 2(2a + 3d).
We are not given the first term (a) of the sequence, so we cannot calculate the exact sum. However, using the formula, we can express the sum in terms of the first term.
Hence, the sum of the first 4 terms of the arithmetic sequence is 2(2a + 3d).