Find the 81st term of the arithmetic sequence 24, 11, -2, ...24,11,−2

The 81st term of arithmetic sequence is -1016

Step-by-step explanation:

Formula for arithmetic sequence is given by,

Where,

Therefore value of n is n = 81.

Common difference is calculated by subtracting second term from first term as follows,

Therefore for first two terms that is 24 and 11 common difference is,

Therefore for next two terms that is 11 and -2 common difference is,

Hence common difference is

Substituting the value,

Simplifying,

Therefore, the 81st term of the arithmetic sequence 24, 11, -2, ... is -1016

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

i dont know

step-by-step explanation: