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.