the sum of the first 7 terms of an arithmetic sequence is 63. if the first term is 3,find d.
+2446 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.
\(S_{7}=7*\frac{a_1+a_7}{2}\\ a_7=a_1+6d\\ 63=\frac{7(2a_1+6d)}{2}\\ 9=a_1+3d\\ 9=3+3d\\ 3=1+d\\ d=2\)
