Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.

I got stuck on this question for six attempts. Therefore I started trying other methods. I started with a10=1 and then subtracted 6 to get a11=-5. I continued this process until I reached a45=-209

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ap8997154 ap8997154 · Answer 2 · 2022-08-09T15:05:48+02:00

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The 45th term for the arithmetic sequence is -209.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

aₙ = a₁ + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

Given that the 10th term of the arithmetic series is 1, while the common difference of the arithmetic series is -6. Therefore, 10th term of the series can also be written as,

aₙ = a₁+(n-1)d

1 = a₁+(10-1)(-6)

1 = a₁ + (9)(-6)

1 = a₁ - 54

a₁ = 55

Now, the 45th term for the arithmetic sequence is,

aₙ = a₁ + (n-1)d

a₄₅ = 55 + (45-1)(-6)

a₄₅ = 55 - 264

a₄₅ = -209

Hence, the 45th term for the arithmetic sequence is -209.

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