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Answer :
Final answer:
The sum of the arithmetic sequence 151, 137, 123, ..., with 26 terms is -624.
Explanation:
To find the sum of an arithmetic sequence, we can use the formula:
S = (n/2)(a + l)
where S is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, we are given the first term (a = 151), the common difference (d = -14), and the number of terms (n = 26).
Using the formula, we can substitute these values into the equation:
S = (26/2)(151 + l)
Since the common difference is -14, we can find the last term (l) by adding the common difference to the first term:
l = a + (n-1)d
l = 151 + (26-1)(-14)
l = 151 + 25(-14)
l = 151 - 350
l = -199
Now we can substitute the values of a and l into the sum formula:
S = (26/2)(151 + (-199))
S = (13)(-48)
S = -624
Therefore, the sum of the arithmetic sequence 151, 137, 123, ... with 26 terms is -624.
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