What is the nth term rule of the linear sequence below? 22 , 18 , 14 , 10 , 6 , . .

The required term rule of sequence is given by  

Step-by-step explanation:

Given: A linear sequence

As per question,

First term of sequence is .

Second term of sequence is 18,

Third term of sequnce is 14.

For a sequence to be in A.P, its common difference must be same for all terms.

Common difference

Now, term of sequence is given by

Therefore,   term of sequence is

Hence,   term rule of sequence is given by  .

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Step-by-step explanation:

The nth term of an AP is

where, a is the first term of the sequence and d is common difference.

The given linear sequence is

22 , 18 , 14 , 10 , 6 , . . .

Here, first term is 22 and common difference is

The common difference of the sequence is -4. So, the nth term of given sequence is

Therefore, the nth term of the sequence is .

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step-by-step explanation:

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.