Answer :

Final answer:

The 81st term of the arithmetic sequence is -1210, calculated using the formula for the nth term of an arithmetic sequence with the first term -10 and the common difference -15.

Explanation:

To find the 81st term of the arithmetic sequence -10, -25, -40, we need to use the formula for the nth term of an arithmetic sequence: aₙ = a₁ + (n - 1)d, where aₙ is the nth term, a₁ is the first term, and d is the common difference between the terms.

In this sequence, the first term a_1 is -10, and the common difference d can be determined by subtracting the first term from the second term (-25 - (-10) = -15).

Therefore, the common difference d is -15. Using this information:

a₈₁ = -10 + (81 - 1)(-15)
= -10 + (80)(-15)
= -10 - 1200
= -1210

The 81st term of the sequence is -1210.

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Rewritten by : Barada

The 81st term of the arithmetic sequence -10, -25, -40, ... is -1210

Here is a step-by-step explanation The common difference in this sequence,

d = a2 -a1

let a2 = -25 and a1 = -10

d= -25 - (-10)

d = -15

the common difference (d) = -15

To find the n term we use :

an= a1+ (n-1)d

Therefore,

a81 = -10 + (81-1)(-15)

= -1210

The 81stterm of the arithmetic sequence -10, -25, -40, ... -1210

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