Respuesta :
Answer:
The 81st term of arithmetic sequence is -1016
Step-by-step explanation:
Formula for arithmetic sequence is given by,
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Where,
[tex]a_n=n^{th} \:term\:of\:sequence=a_81[/tex]
Therefore value of n is n = 81.
[tex]a_1=1^{st} \:term\:of\:sequence=24[/tex]
[tex]d=common\:difference[/tex]
Common difference is calculated by subtracting second term from first term as follows,
[tex]d=a_{n+1}-a_{n}[/tex]
Therefore for first two terms that is 24 and 11 common difference is,
[tex]d=11-24=-13[/tex]
Therefore for next two terms that is 11 and -2 common difference is,
[tex]d=-2-11=-13[/tex]
Hence common difference is [tex]d=-13[/tex]
Substituting the value,
[tex]a_{81}=24+13\left(81-1\right)[/tex]
Simplifying,
[tex]a_{81}=24+\left(-13\right)\left(81-1\right)[/tex]
[tex]a_{81}=24+\left(-1040\right)[/tex]
[tex]a_{81}=24-1040[/tex]
[tex]a_{81}=-1016[/tex]
Therefore, the 81st term of the arithmetic sequence 24, 11, -2, ... is -1016
