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The sum of the first 8 term of arithmetic sequence is 104 , and the sum of the next 12 terms is 636, then find the common difference and the general term

User Smilediver
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Final answer:

The common difference is 10 and the general term is a_n = 13 + 10(n - 1).

Step-by-step explanation:

To find the common difference and the general term of the arithmetic sequence, we can use the formula for the sum of an arithmetic series:



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



Where Sum is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.



From the given information, we have:



Sum of the first 8 terms = 104
Sum of the next 12 terms = 636



Substituting these values into the formula, we get:



(8/2)(2a + 7d) = 104



(12/2)(2a + 11d) = 636



Simplifying the equations, we have:



4a + 14d = 104



6a + 33d = 636



Now we can solve these equations simultaneously to find the values of a and d. Solving the equations, we find that a = 13 and d = 10.



Therefore, the common difference is 10 and the general term of the arithmetic sequence is an = 13 + 10(n - 1).

User Amine Hajyoussef
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