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# arithmetic sequence

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the sum of the first 7 terms of an arithmetic sequence is 63. if the first term is 3,find d.

May 16, 2020

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An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

The sum of n terms of an arithmetic sequence can be found with the formula $$S_n=n*\frac{a_1+a_n}{2}$$.

The term $$a_n$$ can be found with the following formula $$a_n=a_1+d(n-1)$$. When we put these formulas together, we can solve for d.

$$S_{7}=7*\frac{a_1+a_7}{2}\\ a_7=a_1+6d\\ 63=\frac{7(2a_1+6d)}{2}\\ 9=a_1+3d\\ 9=3+3d\\ 3=1+d\\ d=2$$

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May 16, 2020