Question

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

Answer 1

Answer:

The 81st term of arithmetic sequence is -1016

Step-by-step explanation:

Formula for arithmetic sequence is given by,

$a_n=a_1+\left(n-1\right)d$

Where,

$a_n=n^{th} \:term\:of\:sequence=a_81$

Therefore value of n is n = 81.

$a_1=1^{st} \:term\:of\:sequence=24$

$d=common\:difference$

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

$d=a_{n+1}-a_{n}$

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

$d=11-24=-13$

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

$d=-2-11=-13$

Hence common difference is $d=-13$

Substituting the value,

$a_{81}=24+13\left(81-1\right)$

Simplifying,

$a_{81}=24+\left(-13\right)\left(81-1\right)$

$a_{81}=24+\left(-1040\right)$

$a_{81}=24-1040$

$a_{81}=-1016$

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