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frez [133]
3 years ago
12

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

Mathematics
1 answer:
FromTheMoon [43]3 years ago
5 0

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

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