In the arithmetic sequence {−9,−4,1,6,11,…}, what is the common difference?

d = 5

Step-by-step explanation:

The common difference (d) is the difference between consecutive terms in the sequence and is calculated as

d = - 4 - (- 9) = 1 - (- 4) = 6 - 1 = 11 - 6 = 5

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.