Find the formula for t(n) for the arithmetic sequence in which t(15) = 10 and t(63) = 106. Homework Help ✎
Visualize the sequences as two points on a graph, (15, 10) and (63, 106).
Finding the common difference is the same as finding the constant rate of change of a line, the slope.
Use the slope or common difference and one of the points, say (15, 10) to substitute into t(n) = mn + b. And solve: 10 = 2(15) + b
t(n) = 2n − 20