Find the sum of the first 9 terms of the sequence. show all work for full credit. 2, -7, -16, -25,

We can see the sequence goes by decreasing 9 on each number

so the numbers are

2, -7, -16, -25, -34, -43, -52, -61, -70

so adding all these numbers we get

2-7-16-25-34-43-52-61-70

= -306

hope this helped

Answer

1 number

explanation

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.

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