Identify the series 2 + 5 + 8 + 11 + 14 + . . as arithmetic, geometric or neither.

Arithmetic Series

Step-by-step explanation:

We are given a series 2 + 5 + 8 + 11 + 14 + . . .

We need to choose which series this one.

For geometric: The common ration is equal.

For arithmetic: The common difference is equal.

Series: 2 + 5 + 8 + 11 + 14 + . . .

Common difference : 5 - 2 = 8 - 5 = 14 - 11 = 3

Here, The common difference is equal.

Hence, The series is arithmetic.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places