Ageometric sequence is defined by the equation an=(2)5-2n. what are the first three terms of the sequence and what is the common ratio, r?

First term = (2)5^(-2*1) =2/25

2nd term = (2)5^(-2*2) = 2/ 625

3rd term = 2(5)^(-2*3) = 2/ 15625

If we divide the 3rd term by the 2nd term or the 2nd term by the first we get the common ratio

Common ratio = 1/25 or 0.04 as a decimal fraction.

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