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Given the sequence -10, 690, 1390, 2090, 2790 Determine its nᵗʰ term

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Final answer:

The nth term of the arithmetic sequence -10, 690, 1390, 2090, 2790 can be found using the formula Tₙ = a + (n-1)d. For this sequence, a = -10 and d = 700, the nth term formula is Tₙ = 700n - 710.

Step-by-step explanation:

The student is tasked with finding the nᵗʰ term of a sequence. Looking at the given sequence -10, 690, 1390, 2090, 2790, it's clear that each term increases by 700 from the previous term. This indicates that the sequence is arithmetic with a common difference of 700.

To find the nᵗʰ term, we'll use the arithmetic sequence formula: Tₙ = a + (n-1)d, where Tₙ is the nᵗʰ term, a is the first term, n is the term number, and d is the common difference.

Applying the values from the sequence: a = -10 and d = 700. Thus, the nᵗʰ term is Tₙ = -10 + (n-1) × 700, which simplifies to Tₙ = 700n - 710. This is the formula for the nᵗʰ term of the given sequence.

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