2,5, 25/2, ...
find the 10th term

The   term of the given sequence

Step-by-step explanation:

Step(i):-

Given sequence   2 , 5,

First term    a = 2

The difference of given geometric sequence

Step(ii):-

The   term of the given sequence

The   term of the given sequence

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.