Find the first three terms of the series represented by the formula 3(- 2)(n - 1).

0, - 6, - 12

Step-by-step explanation:

To find the first 3 terms, substitute n = 1, 2, 3 into the formula

a₁ = 3(- 2)(1 - 1) = 3 × - 2 × 0 = 0

a₂ = 3(- 2)(2 - 1) = 3 × - 2 × 1 = - 6

a₃ = 3(- 2)(3 - 1) = 3 × - 2 × 2 = - 12

First 3 terms are 0, - 6, - 12

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

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.