Find a formula for the general term of the sequence 5 3 , − 6 9 , 7 27 , − 8 81 , 9 243 , assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 5 3 a2 = − 6 9 a3 = 7 27 a4 = − 8 81 a5 = 9 243 .

The formula to the sequence

5/3, -6/9, 7/27, -8/81, 9/243, ...

is

(-1)^n. (4 + n). 3^(-n)

For n = 1, 2, 3, ...

Step-by-step explanation:

The sequence is

5/3, - 6/9, 7/27, - 8/81, 9/243, ...

We notice the following

- That the numbers are alternating between - and +

- That the numerator of a number is one greater than the numerator of the preceding number. The first number being 5.

- That the denominator of a number is 3 raised to the power of (2 minus the position of the number)

Using these observations, we can write a formula for the sequence.

(-1)^n for n = 1, 2, 3, ... takes care of the alternation between + and -

(4 + n) for n = 1, 2, 3, ... takes care of the numerators 5, 6, 7, 8, ...

3^(-n) for n = 1, 2, 3, ... takes care of the denominators 3, 9, 27, 81, 243, ...

Combining these, we have the formula to be

(-1)^n. (4 + n). 3^(-n)

For n = 1, 2, 3, ...

isi

step-by-step explanation:

use that smart brain

let's solve your equation step-by-step.

24−3x=−27

step 1: simplify both sides of the equation.

24−3x=−27

24+−3x=−27

−3x+24=−27

step 2: subtract 24 from both sides.

−3x+24−24=−27−24

−3x=−51

step 3: divide both sides by -3.

−3x

−3

=

−51

−3

x=17

answer:

x=17

step-by-step explanation:

mark brainliest and have a great day!